fg 9 science sa-i all chapters

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1 Matter in OurSurroundingsEverything in this universe is made up of material which scientists have named “matter”. The air we breathe, thefood we eat, stones, clouds, stars, plants and animals, even a small drop of water or a particle of sand– each thingis matter. We can also see as we look around that all the things mentioned above occupy space, that is, volume andhave mass.

ince early times, human beings have been trying to understand their surroundings. Early !ndian philosophersclassified matter in the form of five basic elements – the “ Panch Tatva ”– air, earth, fire, sky and water.

"ccording to them everything, living or nonliving, was made up of these five basic elements. "ncient #reek philosophers had arrived at a similar classification of matter. $odern day scientists have evolved two types of classification of matter based on their physical properties and chemical nature.

Physical Nature of Matter

MATTER IS MADE UP OF PARTIC ES

%or a long time, two schools of thought prevailed regarding the nature of matter. &ne school believed matter to becontinuous like a block of wood, whereas, the other thought that matter was made up of particles like sand. Theremust be millions of tiny particles in 'ust one crystal of potassium permanganate, which keep on dividingthemselves into smaller and smaller particles. (ltimately a stage is reached when the particles cannot dividefurther into smaller particles.

Characteristics of Particles of Matter

PARTIC ES OF MATTER !A"E SPACE #ET$EEN T!EM

)articles of sugar, salt, *ettol, or potassium permanganate get evenly distributed in water when dissolved.imilarly, when we make tea, coffee or lemonade +nimbu paani , particles of one type of matter get into the spaces

between particles of the other. This shows that there is enough space between particles of matter.

PARTIC ES OF MATTER ARE CONTINUOUS % MO"IN&

)articles of matter are continuously moving, that is, they possess what we call the kinetic energy. "s the

temperature rises, particles move faster. o, we can say that with increase in temperature the kinetic energy of theparticles also increases.

When we dissolve sugar or salt in water we observe that particles of matter intermi- on their own with each other.They do so by getting into the spaces between the particles. This intermi-ing of particles of two different types of matter on their own is called diffusion. We also observe that on heating, diffusion becomes faster.

PARTIC ES OF MATTER ATTRACT EAC! OT!ER

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)articles of matter have force acting between them. This force keeps the particles together. The strength of thisforce of attraction varies from one kind of matter to another.

States of Matter

&bserve different types of matter around you. What are its different states We can see that matter around use-ists in three different states– solid, li/uid and gas. These states of matter arise due to the variation in the

characteristics of the particles of matter.

T!E SO ID STATE

olids have a definite shape, distinct boundaries and fi-ed volumes, that is, have negligible compressibility. olidshave a tendency to maintain their shape when sub'ected to outside force. olids may break under force but it isdifficult to change their shape, so they are rigid. " rubber band changes shape under force and regains the sameshape when the force is removed. !f e-cessive force is applied, it breaks. The shape of each individual sugar or saltcrystal remains fi-ed, whether we take it in our hand, put it in a plate or in a 'ar. " sponge has minute holes, in which air is trapped, when we press it, the air is e-pelled out and we are able to compress it.

T!E I'UID STATE

We observe that li/uids have no fi-ed shape but have a fi-ed volume. They take up the shape of the container in which they are kept. 0i/uids flow and change shape, so they are not rigid but can be called fluid. olids and li/uidscan diffuse into li/uids. The gases from the atmosphere diffuse and dissolve in water. These gases, especially o-ygen and carbon dio-ide, are essential for the survival of a/uatic animals and plants.

"ll living creatures need to breathe for survival. The a/uatic animals can breathe under water due to the presenceof dissolved o-ygen in water. Thus, we may conclude that solids, li/uids and gases can diffuse into li/uids. Therate of diffusion of li/uids is higher than that of solids. This is due to the fact that in the li/uid state, particlesmove freely and have greater space between each other as compared to particles in the solid state.

T!E &ASEOUS STATE

1ave you ever observed a balloon seller filling a large number of balloons from a single cylinder of gas En/uirefrom him how many balloons is he able to fill from one cylinder. "sk him which gas does he have in the cylinder.

We have observed that gases are highly compressible as compared to solids and li/uids. The li/uefied petroleumgas +0)# cylinder that we get in our home for cooking or the o-ygen supplied to hospitals in cylinders iscompressed gas. 2ompressed natural gas +23# is used as fuel these days in vehicles. *ue to its highcompressibility, large volumes of a gas can be compressed into a small cylinder and transported easily.

We come to know of what is being cooked in the kitchen without even entering there, by the smell that reaches our

nostrils. 1ow does this smell reach us The particles of the aroma of food mi- with the particles of air spread fromthe kitchen, reach us and even farther away. The smell of hot cooked food reaches us in seconds4 compare this with the rate of diffusion of solids and li/uids. *ue to high speed of particles and large space between them, gasesshow the property of diffusing very fast into other gases.

!n the gaseous state, the particles move about randomly at high speed. *ue to this random movement, theparticles hit each other and also the walls of the container. The pressure e-erted by the gas is because of this forcee-erted by gas particles per unit area on the walls of the container.





Can Matter Change its State(

We all know from our observation that water can e-ist in three states of matter–

• solid, as ice,• li/uid, as the familiar water, and

• gas, as water vapour.

What happens inside the matter during this change of state What happens to the particles of matter during thechange of states 1ow does this change of state take place

EFFECT OF C!AN&E OF TEMPERATURE

&n increasing the temperature of solids, the kinetic energy of the particles increases. *ue to the increase in kineticenergy, the particles start vibrating with greater speed. The energy supplied by heat overcomes the forces of attraction between the particles. The particles leave their fi-ed positions and start moving more freely. " stage isreached when the solid melts and is converted to a li/uid. The temperature at which a solid melts to become ali/uid at the atmospheric pressure is called its melting point.

The )elting *oint of a solid is an indication of the strength of the force of attraction +et,een its*articles-

The melting point of ice is 567.89 :. The process of melting, that is, change of solid state into li/uid state is alsoknown as fusion.

$hen a solid )elts. its te)*erature re)ains the sa)e. so ,here does the heat energy go( ;ou musthave observed, during the e-periment of melting, that the temperature of the system does not change after themelting point is reached, till all the ice melts. This happens even though we continue to heat the beaker, that is, wecontinue to supply heat. This heat gets used up in changing the state by overcoming the forces of attraction between the particles. "s this heat energy is absorbed by ice without showing any rise in temperature, it isconsidered that it gets hidden into the contents of the beaker and is known as the latent heat. The word latentmeans hidden. The amount of heat energy that is re/uired to change 8 kg of a solid into li/uid at atmosphericpressure at its melting point is known as the latent heat of fusion. o, particles in water at <=2 +567 : havemore energy as compared to particles in ice at the same temperature.





When we supply heat energy to water, particles start moving even faster. "t a certain temperature, a point isreached when the particles have enough energy to break free from the forces of attraction of each other. "t thistemperature the li/uid starts changing into gas. The temperature at which a li/uid starts boiling at theatmospheric pressure is known as its boiling point. >oiling is a bulk phenomenon. )articles from the bulk of theli/uid gain enough energy to change into the vapour state.%or water this temperature is 767 : +8<<=2 ? 567 @ 8<<? 767 : .

)articles in steam, that is, water vapour at 767 : +8<<< 2 have more energy than water at the same temperature.This is because particles in steam have absorbed e-tra energy in the form of latent heat of vaporisation.

o, we infer that the state of matter can be changed into another state by changing the temperature. We have learnt that substances around us change state from solid to li/uid and from li/uid to gas on application

of heat. >ut there are some that change directly from solid state to gaseous state and vice versa without changinginto the li/uid state.

" change of state directly from solid to gas without changing into li/uid state +or vice versa is calledsu+li)ation .

EFFECT OF C!AN&E OF PRESSURE

We have already learnt that the difference in various states of matter is due to the difference in the distances between the constituent particles. What will happen when we start putting pressure and compress a gas enclosedin a cylinder Will the particles come closer *o you think that increasing or decreasing the pressure can change

the state of matter

"pplying pressure and reducing temperature can li/uefy gases. 1ave you heard of solid carbon dio-ide +2& 5 !t istored under high pressure. olid 2& 5 gets converted directly to gaseous state on decrease of pressure to 8atmosphere without coming into li/uid state. This is the reason that solid carbon dio-ide is also known as dry iceThus, we can say that pressure and temperature determine the state of a substance, whether it will be solid, li/uidor gas.





!O$ DOES E"APORATION CAUSE COO IN&(

!n an open vessel, the li/uid keeps on evaporating. The particles of li/uid absorb energy from the surrounding toregain the energy lost during evaporation. This absorption of energy from the surroundings make thesurroundings cold.

What happens when you pour some acetone +nail polish remover on your palm The particles gain energy from

your palm or surroundings and evaporate causing the palm to feel cool.

"fter a hot sunny day, people sprinkle water on the roof or open ground because the large latent heat of vaporisation of water helps to cool the hot surface.

$hy should ,e ,ear cotton clothes in su))er(

*uring summer, we perspire more because of the mechanism of our body which keeps us cool. We know thatduring evaporation, the particles at the surface of the li/uid gain energy from the surroundings or body surfaceand change into vapour. The heat energy e/ual to the latent heat of vaporisation is absorbed from the body leavingthe body cool. 2otton, being a good absorber of water helps in absorbing the sweat and e-posing it to theatmosphere for easy evaporation.

$hy do ,e see ,ater dro*lets on the outer surface of a glass containing ice0cold ,ater(

0et us take some iceCcold water in a tumbler. oon we will see water droplets on the outer surface of the tumbler.The water vapour present in air, on coming in contact with the cold glass of water, loses energy and gets convertedto li/uid state, which we see as water droplets.

3ow scientists are talking of five states of matterB olid, 0i/uid, #as, )lasma and >oseCEinstein 2ondensate.

Plas)a1 The state consists of super energetic and super e-cited particles. These particles are in the form of ionised gases. The fluorescent tube and neon sign bulbs consist of plasma. !nside a neon sign bulb there is neongas and inside a fluorescent tube there is helium gas or some other gas. The gas gets ionised, that is, gets charged when electrical energy flows through it. This charging up creates a plasma glowing inside the tube or bulb. Theplasma glows with a special colour depending on the nature of gas. The un and the stars glow because of thepresence of plasma in them. The plasma is created in stars because of very high temperature.

#ose0Einstein Condensate1 !n 8D5<, !ndian physicist atyendra 3ath >ose had done some calculations for afifth state of matter. >uilding on his calculations, "lbert Einstein predicted a new state of matter – the >oseCEinstein 2ondensate +>E2 . !n 5<<8, Eric ". 2ornell, Wolfgang :etterle and 2arl E. Wieman of ( " received the3obel pri e in physics for achieving “>oseCEinstein condensation”. The >E2 is formed by cooling a gas of e-tremely low density, about oneChundredCthousandth the density of normal air, to super low temperatures.





" solution has a solvent and a solute as its components. The component of the solution that dissolves the othercomponent in it +usually the component present in larger amount is called the solvent. The component of thesolution that is dissolved in the solvent +usually present in lesser /uantity is called the solute.

Pro*erties of a solution

• " solution is a homogeneous mi-ture.•

The particles of a solution are smaller than 8 nm +8<CD metre in diameter. o, they cannot be seen by naked eyes.

• >ecause of very small particle si e, they do not scatter a beam of light passing through the solution. o, thepath of light is not visible in a solution.

• The solute particles cannot be separated from the mi-ture by the process of filtration. The solute particlesdo not settle down when left undisturbed, that is, a solution is stable.

Concentration of a Solution• !n activity 5.5, we observed that groups " and > obtained different shades of solutions. o, we understand

that in a solution the relative proportion of the solute and solvent can be varied. *epending upon the

amount of solute present in a solution, it can be called a dilute, concentrated or a saturated solution.*ilute and concentrated are comparative terms. !n activity 5.5, the solution obtained by group " is diluteas compared to that obtained by group >.

• !s the amount of salt and sugar or barium chloride, that can be dissolved in water at a given temperature,the same "t any particular temperature, a solution that has dissolved as much solute as it is capable of dissolving, is said to be a saturated solution. !n other words, when no more solute can be dissolved in asolution at a given temperature, it is called a saturated solution. The amount of the solute present in thesaturated solution at this temperature is called its solubility.

• !f the amount of solute contained in a solution is less than the saturation level, it is called an unsaturatedsolution.

• What would happen if you were to take a saturated solution at a certain temperature and cool it slowly. We can infer from the above activity that different substances in a given solvent have different solubilitiesat the same temperature.

• The concentration of a solution is the amount of solute present in a given amount +mass or volume of solution, or the amount of solute dissolved in a given mass or volume of solvent.

• Concentration of solution ? Amount of solute / Amount of solution• &r

• Amount of solute /Amount of solvent • There are various ways of e-pressing the concentration of a solution, but here we will learn only two

methods.

$hat is a Sus*ension(

3onChomogeneous systems, like those in which solids are dispersed in li/uids, are called suspensions. " suspension is a heterogeneous mi-ture in which the solute particles do not dissolve but remain suspendedthroughout the bulk of the medium. )articles of a suspension are visible to the naked eye.





Pro*erties of a Sus*ension

• uspension is a heterogeneous mi-ture.• The particles of a suspension can be seen by the naked eye.

• The particles of a suspension scatter a beam of light passing through it and make its path visible.

• The solute particles settle down when a suspension is left undisturbed, that is, a suspension is unstable.They can be separated from the mi-ture by the process of filtration.

$hat is a Colloidal Solution(

The mi-ture obtained by group * in activity 5.5 is called a colloid or a colloidal solution. The particles of a colloidare uniformly spread throughout the solution. *ue to the relatively smaller si e of particles, as compared to that of a suspension, the mi-ture appears to be homogeneous. >ut actually, a colloidal solution is a heterogeneousmi-ture, for e-ample, milk.

>ecause of the small si e of colloidal particles, we cannot see them with naked eyes. >ut, these particles can easily scatter a beam of visible light as observed in activity 5.5. This scattering of a beam of light is called the Tyndall

effect after the name of the scientist who discovered this effect.

Tyndall effect can also be observed when a fine beam of light enters a room through a small hole. This happensdue to the scattering of light by the particles of dust and smoke in the air.

Tyndall effect can be observed when sunlight passes through the canopy of a dense forest. !n the forest, mistcontains tiny droplets of water, which act as particles of colloid dispersed in air.





Pro*erties of a colloid

8. " colloid is a heterogeneous mi-ture.5. The si e of particles of a colloid is too small to be individually seen by naked eyes.

7. 2olloids are big enough to scatter a beam of light passing through it and make its path visible.

I. They do not settle down when left undisturbed, that is, a colloid is /uite stable.

J. They cannot be separated from the mi-ture by the process of filtration. >ut, a special techni/ue of separation known as centrifugation, can be used to separate the colloidal particles.

The components of a colloidal solution are the dispersed phase and the dispersion medium. The soluteClikecomponent or the dispersed particles in a colloid form the dispersed phase, and the component in which thedispersed phase is suspended is known as the dispersing medium. 2olloids are classified according to the state+solid, li/uid or gas of the dispersing medium and the dispersed phase. " few common e-amples are given inTable 8. %rom this table you can see that they are very common everyday life.

Table 1: Common examples of colloids

Dispersed phase Dispersing Medium Type Example

Liquid Gas Aerosol Fog, clouds, mist

Solid Gas Aerosol Smoke, automobile exhaust

Gas Liquid Foam Shaving cream

Liquid Liquid Emulsion Milk, face cream





Solid Liquid Sol Milk of magnesia, mud

Gas Solid Foam Foam, rubber, sponge, pumice

Liquid Solid Gel ell!, cheese, butter

Solid Solid Solid Sol "oloured gemstone, milk! glass

Se*arating the Co)*onents of a Mi3ture

We have learnt that most of the natural substances are not chemically pure. *ifferent methods of separation areused to get individual components from a mi-ture. eparation makes it possible to study and use the individualcomponents of a mi-ture. 1eterogeneous mi-tures can be separated into their respective constituents by simplephysical methods like handpicking, sieving, filtration that we use in our dayCtoCday life. ometimes specialtechni/ues have to be used for the separation of the components of a mi-ture.

!o, can $e O+tain Coloured Co)*onent 5Dye6 fro) #lue 7 #lac8 In8(• %ill half a beaker with water.• )ut a watch glass on the mouth of the beaker +%ig. J .

• )ut few drops of ink on the watch glass.

• 3ow start heating the beaker. We do not want to heat the ink directly. ;ou will see that evaporation istaking place from the watch glass.

• 2ontinue heating as the evaporation goes on and stop heating when you do not see any further change onthe watch glass.

• &bserve carefully and record your observations.

We find that ink is a mi-ture of a dye in water. Thus, we can separate the volatile component +solvent from itsnonCvolatile solute by the method of evaporation

!o, can $e Se*arate Crea) Fro) Mil8(





3owCaCdays, we get fullCcream, toned and doubleCtoned varieties of milk packed in polypacks or tetra packs in themarket. These varieties of milk contain different amounts of fat.

• Take some fullCcream milk in a test tube.• 2entrifuge it by using a centrifuging machine for two minutes. !f a centrifuging machine is not available in

the school, you can do this activity at home by using a milk churner, used in the kitchen.

ometimes the solid particles in a li/uid are very small and pass through a filter paper. %or such particles thefiltration techni/ue cannot be used for separation. uch mi-tures are separated by centrifugation. The principle isthat the denser particles are forced to the bottom and the lighter particles stay at the top when spun rapidly.

!o, can $e Se*arate a Mi3ture of T,o I))isci+le i9uids(• 0et us try to separate kerosene oil from water using a separating funnel.• )our the mi-ture of kerosene oil and water in a separating funnel +%ig. 9 .

• 0et it stand undisturbed for sometime so that separate layers of oil and water are formed.

• &pen the stopcock of the separating funnel and pour out the lower layer of water carefully.

•

2lose the stopcock of the separating funnel as the oil reaches the stopCcock.

A**lications

• To separate mi-ture of oil and water.• !n the e-traction of iron from its ore, the lighter slag is removed from the top by this method to leave the

molten iron at the bottom in the furnace.

The principle is that immiscible li/uids separate out in layers depending on their densities.

!o, can $e Se*arate a Mi3ture of Salt and A))oniu) Chloride(





We have learnt that ammonium chloride changes directly from solid to gaseous state on heating. o, to separatesuch mi-tures that contain a sublimable volatile component from a nonCsublimable impurity +salt in this case , thesublimation process is used +%ig.6 . ome e-amples of solids which sublime are ammonium chloride, camphor,naphthalene and anthracene.

Is the Dye in #lac8 In8 a Single Colour(• Take a thin strip of filter paper.• *raw a line on it using a pencil, appro-imately 7 cm above the lower edge K%ig.L +a M.

• )ut a small drop of ink +water soluble, that is, from a sketch pen or fountain pen at the centre of the line.0et it dry.

• 0ower the filter paper into a 'arNglassN beakerNtest tube containing water so that the drop of ink on thepaper is 'ust above the water level, as shown in %ig. L+b and leave it undisturbed.

• Watch carefully, as the water rises up on the filter paper. Aecord your observations.





The ink that we use has water as the solvent and the dye is soluble in it. "s the water rises on the filter paper ittakes along with it the dye particles. (sually, a dye is a mi-ture of two or more colours. The coloured componentthat is more soluble in water, rises faster and in this way the colours get separated.

This process of separation of components of a mi-ture is known as chromatography. :roma in #reek meanscolour. This techni/ue was first used for separation of colours, so this name was given. 2hromatography is thetechni/ue used for separation of those solutes that dissolve in the same solvent. With the advancement intechnology, newer techni/ues of chromatography have been developed.

A**licationsTo separate

• colours in a dye• pigments from natural colours

• drugs from blood

!o, can $e Se*arate a Mi3ture of T,o Misci+le i9uids(• 0et us try to separate acetone and water from their mi-ture.• Take the mi-ture in a distillation flask. %it it with a thermometer.

• "rrange the apparatus as shown in %ig. D.

• 1eat the mi-ture slowly keeping a close watch at the thermometer.

• The acetone vaporises, condenses in the condenser and can be collected from the condenser outlet.

•

Water is left behind in the distillation flask.





!o, can $e O+tain Different &ases fro) Air(

"ir is a homogeneous mi-ture and can be separated into its components by fractional distillation. The flow diagram +%ig. 88 shows the steps of the process.





!f we want o-ygen gas from air +%ig.85 , we have to separate out all the other gases present in the air. The air iscompressed by increasing the pressure and is then cooled by decreasing the temperature to get li/uid air. Thisli/uid air is allowed to warmCup slowly in a fractional distillation column, where gases get separated at differentheights depending upon their boiling points.





Physical and Che)ical Changes

To understand the difference between a pure substance and a mi-ture, let us understand the difference between aphysical and a chemical change. We have learnt about a few physical properties of matter. The properties that can be observed and specified like colour, hardness, rigidity, fluidity, density, melting point, boiling point etc. are thephysical properties.

The interCconversion of states is a physical change because these changes occur without a change in compositionand no change in the chemical nature of the substance. "lthough ice, water and water vapour all look different anddisplay different physical properties, they are chemically the same.

>oth water and cooking oil are li/uid but their chemical characteristics are different. They differ in odour andinflammability. We know that oil burns in air whereas water e-tinguishes fire. !t is this chemical property of oilthat makes it different from water. >urning is a chemical change. *uring this process one substance reacts withanother to undergo a change in chemical composition. 2hemical change brings change in the chemical propertiesof matter and we get new substances. " chemical change is also called a chemical reaction. *uring burning of acandle, both physical and chemical changes take place.

$hat are the Ty*es of Pure Su+stances(

&n the basis of their chemical composition, substances can be classified either as elements or compounds.

E EMENTS

Aobert >oyle was the first scientist to use the term element in 8998. "ntoine 0aurent 0avoisier +86I7CDI , a %renchchemist, was the first to establish an e-perimentally useful definition of an element. 1e defined an element as a basic form of matter that cannot be broken down into simpler substances by chemical reactions.

Elements can be normally divided into metals, nonCmetals and metalloids.

$etals usually show some or all of the following propertiesB

• They have a lustre +shine .• They have silveryCgrey or goldenCyellow colour.

• They conduct heat and electricity.

• They are ductile +can be drawn into wires .





• They are malleable +can be hammered into thin sheets .

• They are sonorous +make a ringing sound when hit .

E-amples of metals are gold, silver, copper, iron, sodium, potassium etc. $ercury is the only metal that is li/uid atroom temperature.

3onCmetals usually show some or all of the following propertiesB

• They display a variety of colours.• They are poor conductors of heat and electricity.

• They are not lustrous, sonorous or malleable.

E-amples of nonCmetals are hydrogen, o-ygen, iodine, carbon +coal, coke , bromine, chlorine etc. ome elementshave intermediate properties between those of metals and nonCmetals, they are called metalloids4 e-amples are boron, silicon, germanium etc.

• The number of elements known at present are more than 8<<. 3inetyCtwo elements are naturally occurring and the rest are manmade.

• $a'ority of the elements are solid.

• Eleven elements are in gaseous state at room temperature.

• Two elements are li/uid at room temperature–mercury and bromine.

• Elements, gallium and cesium become li/uid at a temperature slightly above room temperature +7<7 : .

COMPOUNDS

" compound is a substance composed of two or more elements, chemically combined with one another in a fi-edproportion.





: The Funda)ental Unit of ife While e-amining a thin slice of cork, Aobert 1ooke saw that the cork resembled the structure of a honeycombconsisting of many little compartments. 2ork is a substance which comes from the bark of a tree. This was in the

year 899J when 1ooke made this chance observation through a selfCdesigned microscope. Aobert 1ooke calledthese bo-es cells. 2ell is a 0atin word for Fa little roomG.

This may seem to be a very small and insignificant incident but it is very important in the history of science. This was the very first time that someone had observed that living things appear to consist of separate units. The use of the word FcellG to describe these units is used till this day in biology.

Cell in i/ing Organis)s

Take a small piece from an onion bulb. With the help of a pair of forceps, we can peel off the skin +calledepidermis from the concave side +inner layer of the onion. This layer can be put immediately in a watchCglasscontaining water. This will prevent the peel from getting folded or getting dry. Take a glass slide, put a drop of water on it and transfer a small piece of the peel from the watch glass to the slide. $ake sure that the peel isperfectly flat on the slide. " thin camel hair paintbrush might be necessary to help transfer the peel. 3ow put adrop of iodine solution on this piece followed by a cover slip. Take care to avoid air bubbles while putting the coverslip with the help of a mounting needle. "sk your teacher for help. We have prepared a temporary mount of onionpeel. We can observe this slide under low power followed by high powers of a compound microscope.





We draw the structures that we are able to see through the microscope, on an observation sheet it looks like %ig.5.These structures look similar to each other. Together they form a big structure like an onion bulbO We find fromthis activity that onion bulbs of different si es have similar small structures visible under a microscope. The cellsof the onion peel will all look the same, regardless of the si e of the onion they came from.

These small structures that we see are the basic building units of the onion bulb. These structures are called cells.3ot only onions, but all organisms that we observe around are made up of cells. 1owever, there are also singlecells that live on their own.

2ells were first discovered by Aobert 1ooke in 899J. 1e observed the cells in a cork slice with the help of aprimitive microscope. 0eeuwenhoek +896I , with the improved microscope, discovered the free living cells in pond water for the first time. !t was Aobert >rown in 8L78 who discovered the nucleus in the cell. )urkin'e in 8L7Dcoined the term FprotoplasmG for the fluid substance of the cell. The cell theory, that all the plants and animals arecomposed of cells and that the cell is the basic unit of life, was presented by two biologists, chleiden +8L7L and

chwann +8L7D . The cell theory was further e-panded by Pirchow +8LJJ by suggesting that all cells arise from

preCe-isting cells. With the discovery of the electron microscope in 8DI<, it was possible to observe andunderstand the comple- structure of the cell and its various organelles.

The invention of magnifying lenses led to the discovery of the microscopic world. !t is now known that a single cellmay constitute a whole organism as in "moeba, 2hlamydomonas, )aramoecium and bacteria. These organismsare called unicellular organisms +uni ? single . &n the other hand, many cells group together in a single body andassume different functions in it to form various body parts in multicellular organisms +multi ? many such assome fungi, plants and animals.

Every multiCcellular organism has come from a single cell. 2ells divide to produce cells of their own kind. "ll cellsthus come from preCe-isting cells. ome organisms can also have cells of different kinds. 0ook at the followingpicture. !t depicts some cells from the human body.





The shape and si e of cells are related to the specific function they perform. ome cells like "moeba have changingshapes. !n some cases the cell shape could be more or less fi-ed and peculiar for a particular type of cell4 fore-ample, nerve cells have a typical shape.

Each living cell has the capacity to perform certain basic functions that are characteristic of all living forms. Weknow that there is a division of labour in multicellular organisms such as human beings. This means that differentparts of the human body perform different functions. The human body has a heart to pump blood, a stomach todigest food and so on. imilarly, division of labour is also seen within a single cell in many cases. !n fact, each suchcell has got certain specific components within it known as cell organelles. Each kind of cell organelle performs aspecial function, such as making new material in the cell, clearing up the waste material from the cell and so on. " cell is able to live and perform all its functions because of these organelles. These organelles together constitute

the basic unit called the cell. !t is interesting that all cells are found to have the same organelles, no matter whattheir function is or what organism they are found in.

Structural Organisation of a Cell

We saw above that the cell has special components called organelles. !f we study a cell under a microscope, we would come across three features in almost every cell4 plasma membrane, nucleus and cytoplasm. "ll activitiesinside the cell and interactions of the cell with its environment are possible due to these features.

Plas)a Me)+rane or Cell Me)+rane

This is the outermost covering of the cell that separates the contents of the cell from its e-ternal environment. Theplasma membrane allows or permits the entry and e-it of some materials in and out of the cell. !t also preventsmovement of some other materials. The cell membrane, therefore, is called a selectively permeable membrane.

ome substances like carbon dio-ide or o-ygen can move across the cell membrane by a process called diffusion. We have studied the process of diffusion before. We saw that there is spontaneous movement of a substance froma region of high concentration to a region where its concentration is low.

omething similar to this happens in cells when, for e-ample, some substance like 2& 5 +which is cellular wasteand re/uires to be e-creted out by the cell accumulates in high concentrations inside the cell. !n the cellGs e-ternal





environment, the concentration of 2& 5 is low as compared to that inside the cell. "s soon as there is a difference of concentration of 2& 5 inside and outside a cell, 2& 5 moves out of the cell, from a region of high concentration, to aregion of low concentration outside the cell by the process of diffusion. imilarly, & 5 enters the cell by the processof diffusion when the level or concentration of & 5 inside the cell decreases. Thus, diffusion plays an important rolein gaseous e-change between the cells as well as the cell and its e-ternal environment.

Water also obeys the law of diffusion. The movement of water molecules through such a selectively permeable

membrane is called osmosis. The movement of water across the plasma membrane is also affected by the amountof substance dissolved in water. Thus, osmosis is the passage of water from a region of high water concentrationthrough a semiCpermeable membrane to a region of low water concentration.

&ne of the following three things could happen if we put an animal cell or a plant cell into a solution of sugar orsalt in waterB

8. !f the medium surrounding the cell has a higher water concentration than the cell, meaning that theoutside solution is very dilute, the cell will gain water by osmosis. uch a solution is known as a hypotonicsolution. Water molecules are free to pass across the cell membrane in both directions, but more water will comeinto the cell than will leave. The net +overall result is that water enters the cell. The cell is likely to swellup.

5. !f the medium has e-actly the same water concentration as the cell, there will be no net movement of water across the cell membrane. uch a solution is known as an isotonic solution. Water crosses the cell membrane in both directions, but the amount going in is the same as the amountgoing out, so there is no overall movement of water. The cell will stay the same si e.

7. !f the medium has a lower concentration of water than the cell, meaning that it is a very concentratedsolution, the cell will lose water by osmosis. uch a solution is known as a hypertonic solution. "gain, water crosses the cell membrane in both directions, but this time more water leaves the cell thanenters it. Therefore the cell will shrink.

Thus, osmosis is a special case of diffusion through a selectively permeable membrane.

(nicellular freshwater organisms and most plant cells tend to gain water through osmosis. "bsorption of water by plant roots is also an e-ample of osmosis. Thus, diffusion is important in e-change of gases and water in the life of a cell. !n additions to this, the cell also obtains nutrition from its environment. *ifferent molecules move in andout of the cell through a type of transport re/uiring use of energy in the form of "T).

The plasma membrane is fle-ible and is made up of organic molecules called lipids and proteins. 1owever, we canobserve the structure of the plasma membrane only through an electron microscope. The fle-ibility of the cellmembrane also enables the cell to engulf in food and other material from its e-ternal environment. uch processesare known as endocytosis. "moeba ac/uires its food through such processes.

Cell $all

)lant cells, in addition to the plasma membrane, have another rigid outer covering called the cell wall. The cell wall lies outside the plasma membrane. The plant cell wall is mainly composed of cellulose. 2ellulose is a comple-substance and provides structural strength to plants. When a living plant cell loses water through osmosis there isshrinkage or contraction of the contents of the cell away from the cell wall. This phenomenon is known asplasmolysis.

2ell walls permit the cells of plants, fungi and bacteria to withstand very dilute +hypotonic e-ternal media without bursting. !n such media the cells tend to take up water by osmosis. The cell swells, building up pressure against





the cell wall. The wall e-erts an e/ual pressure against the swollen cell. >ecause of their walls, such cells can withstand much greater changes in the surrounding medium than animal cells

Nucleus

Aemember the temporary mount of onion peel we prepared. We had put iodine solution on the peel. %urther, when we put iodine solution on the peel, each cell did not get evenly coloured. "ccording to their chemical

composition different regions of cells get coloured differentially. ome regions appear darker than other regions. "part from iodine solution we could also use safranin solution or methylene blue solution to stain the cells.

There was a darkly coloured, spherical or oval, dotClike structure near the centre of each cell. This structure iscalled nucleus. The nucleus has a double layered covering called nuclear membrane. The nuclear membrane haspores which allow the transfer of material from inside the nucleus to its outside, that is, to the cytoplasm.

The nucleus contains chromosomes, which are visible as rodCshaped structures only when the cell is about todivide. 2hromosomes contain information for inheritance of features from parents to ne-t generation in the formof *3" +*eo-yribo 3ucleic "cid molecules. 2hromosomes are composed of *3" and protein. *3" moleculescontain the information necessary for constructing and organising cells. %unctional segments of *3" are calledgenes. !n a cell which is not dividing, this *3" is present as part of chromatin material. 2hromatin material is visible as entangled mass of thread like structures. Whenever the cell is about to divide, the chromatin materialgets organised into chromosomes. The nucleus plays a central role in cellular reproduction, the process by which asingle cell divides and forms two new cells. !t also plays a crucial part, along with the environment, in determiningthe way the cell will develop and what form it will e-hibit at maturity, by directing the chemical activities of thecell.

!n some organisms like bacteria, the nuclear region of the cell may be poorly defined due to the absence of anuclear membrane. uch an undefined nuclear region containing only nucleic acids is called a nucleoid. uchorganisms, whose cells lack a nuclear membrane, are called prokaryotes +)ro ? primitive or primary4 karyote Qkaryon ? nucleus . &rganisms with cells having a nuclear membrane are called eukaryotes.

Cyto*las)

When we look at the temporary mounts of onion peel as well as human cheek cells, we can see a large region of each cell enclosed by the cell membrane. This region takes up very little stain. !t is called the cytoplasm. Thecytoplasm is the fluid content inside the plasma membrane. !t also contains many specialised cell organelles. Eachof these organelles performs a specific function for the cell.

2ell organelles are enclosed by membranes. !n prokaryotes, beside the absence of a defined nuclear region, themembraneCbound cells organelles are also absent. &n the other hand, the eukaryotic cells have nuclear membraneas well as membraneCenclosed organelles. The significance of membranes can be illustrated with the e-ample of



)rokaryotic cells +see %ig. I also lack most of theother cytoplasmic organelles present in eukaryoticcells. $any of the functions of such organelles arealso performed by poorly organised parts of thecytoplasm. The chlorophyll in photosyntheticprokaryotic bacteria is associated with membranous

vesicles +bag like structures but not with plastids asin eukaryotic cells



viruses. Piruses lack any membranes and hence do not show characteristics of life until they enter a living body and use its cell machinery to multiply.

Cell Organelles

Every cell has a membrane around it to keep its own contents separate from the e-ternal environment. 0arge andcomple- cells, including cells from multicellular organisms, need a lot of chemical activities to support their

complicated structure and function. To keep these activities of different kinds separate from each other, these cellsuse membraneCbound little structures +or ForganellesG within themselves. This is one of the features of theeukaryotic cells that distinguish them from prokaryotic cells. ome of these organelles are visible only with anelectron microscope.

ome important e-amples of cell organelles which we will discuss now areB endoplasmic reticulum, #olgiapparatus, lysosomes, mitochondria, plastids and vacuoles. They are important because they carry out some very crucial functions in cells.

5i6 ENDOPLASMIC RETICULUM (ER)

The endoplasmic reticulum +EA is a large network of membraneCbound tubes and sheets. !t looks like longtubules or round or oblong bags +vesicles . The EA membrane is similar in structure to the plasma membrane.There are two types of EA– rough endoplasmic reticulum +AEA and smooth endoplasmic reticulum + EA . AEA looks rough under a microscope because it has particles called ribosomes attached to its surface. The ribosomes, which are present in all active cells, are the sites of protein manufacture. The manufactured proteins are then sentto various places in the cell depending on need, using the EA. The EA helps in the manufacture of fat molecules,or lipids, important for cell function. ome of these proteins and lipids help in building the cell membrane. Thisprocess is known as membrane biogenesis. ome other proteins and lipids function as en ymes and hormones. "lthough the EA varies greatly in appearance in different cells, it always forms a network system.

Thus, one function of the EA is to serve as channels for the transport of materials +especially proteins between various regions of the cytoplasm or between the cytoplasm and the nucleus. The EA also functions as a





cytoplasmic framework providing a surface for some of the biochemical activities of the cell. !n the liver cells of the group of animals called vertebrates, EA plays a crucial role in deto-ifying many poisons and drugs.

5ii6 GOLGI APPARATUS

The #olgi apparatus, first described by 2amillo #olgi, consists of a system of membraneCbound vesicles arrangedappro-imately parallel to each other in stacks called cisterns. These membranes often have connections with themembranes of EA and therefore constitute another portion of a comple- cellular membrane system. The materialsynthesised near the EA is packaged and dispatched to various targets inside and outside the cell through the#olgi apparatus. !ts functions include the storage, modification and packaging of products in vesicles. !n somecases, comple- sugars may be made from simple sugars in the #olgi apparatus. The #olgi apparatus is alsoinvolved in the formation of lysosomes.

5iii6 LYSOSOMES

0ysosomes are a kind of waste disposal system of the cell. 0ysosomes help to keep the cell clean by digesting any foreign material as well as wornCout cell organelles. %oreign materials entering the cell, such as bacteria or food, as well as old organelles end up in the lysosomes, which break them up into small pieces. 0ysosomes are able to dothis because they contain powerful digestive en ymes capable of breaking down all organic material. *uring thedisturbance in cellular metabolism, for e-ample, when the cell gets damaged, lysosomes may burst and theen ymes digest their own cell. Therefore, lysosomes are also known as the Fsuicide bagsG of a cell. tructurally,lysosomes are membraneCbound sacs filled with digestive en ymes. These en ymes are made by AEA.





5i/6 MITOCHONDRIA

$itochondria are known as the powerhouses of the cell. The energy re/uired for various chemical activitiesneeded for life is released by mitochondria in the form of "T) +"denosine triphopshate molecules. "T) is knownas the energy currency of the cell. The body uses energy stored in "T) for making new chemical compounds andfor mechanical work. $itochondria have two membrane coverings instead of 'ust one. The outer membrane is very porous while the inner membrane is deeply folded. These folds create a large surface area for "T)Cgenerating

chemical reactions.

$itochondria are strange organelles in the sense that they have their own *3" and ribosomes. Therefore,mitochondria are able to make some of their own proteins.

5/6 PLASTIDS

)lastids are present only in plant cells. There are two types of plastids – chromoplasts +coloured plastids andleucoplasts +white or colourless plastids . )lastids containing the pigment chlorophyll are known as chloroplasts.2hloroplasts are important for photosynthesis in plants. 2hloroplasts also contain various yellow or orangepigments in addition to chlorophyll. 0eucoplasts are primarily organelles in which materials such as starch, oilsand protein granules are stored.

The internal organisation of the plastids consists of numerous membrane layers embedded in a material called thestroma. )lastids are similar to mitochondria in e-ternal structure. 0ike the mitochondria, plastids also have theirown *3" and ribosomes.

5/i6 VACUOLES

Pacuoles are storage sacs for solid or li/uid contents. Pacuoles are small si ed in animal cells while plant cellshave very large vacuoles. The central vacuole of some plant cells may occupy J<CD<H of the cell volume. !n plantcells vacuoles are full of cell sap and provide turgidity and rigidity to the cell. $any substances of importance inthe life of the plant cell are stored in vacuoles. These include amino acids, sugars, various organic acids and someproteins. !n singleCcelled organisms like Amoeba , the food vacuole contains the food items that the Amoeba hasconsumed. !n some unicellular organisms, specialised vacuoles also play important roles in e-pelling e-cess waterand some wastes from the cell.

Each cell thus ac/uires its structure and ability to function because of the organisation of its membrane andorganelles in specific ways. The cell thus has a basic structural organisation. This helps the cells to performfunctions like respiration, obtaining nutrition, and clearing of waste material, or forming new proteins. Thus, thecell is the fundamental structural unit of living organisms. !t is also the basic functional unit of life





; Motion!n everyday life, we see some ob'ects at rest and others in motion. >irds fly, fish swim, blood flows through veinsand arteries and cars move. "toms, molecules, planets, stars and gala-ies are all in motion. We often perceive an

ob'ect to be in motion when its position changes with time. 1owever, there are situations where the motion isinferred through indirect evidences.

%or e-ample, we infer the motion of air by observing the movement of dust and the movement of leaves and branches of trees. "n ob'ect may appear to be moving for one person and stationary for some other. %or thepassengers in a moving bus, the roadside trees appear to be moving backwards. " person standing on the road–side perceives the bus alongwith the passengers as moving. 1owever, a passenger inside the bus sees his fellow passengers to be at rest. $ost motions are comple-. ome ob'ects may move in a straight line, others may take acircular path. ome may rotate and a few others may vibrate. There may be situations involving a combination of these.

Descri+ing Motion

We describe the location of an ob'ect by specifying a reference point. 0et us understand this by an e-ample. 0et usassume that a school in a village is 5 km north of the railway station. We have specified the position of the school with respect to the railway station. !n this e-ample, the railway station is the reference point. We could have alsochosen other reference points according to our convenience. Therefore, to describe the position of an ob'ect weneed to specify a reference point called the origin.

MOTION A ON& A STRAI&!T INE

The simplest type of motion is the motion along a straight line. We shall first learn to describe this by an e-ample.2onsider the motion of an ob'ect moving along a straight path. The ob'ect starts its 'ourney from & which istreated as its reference point +%ig.8 . 0et ", > and 2 represents the position of the ob'ect at different instants. "tfirst, the ob'ect moves through 2 and > and reaches ". Then it moves back along the same path and reaches 2through >.

The total path length covered by the ob'ect is &" @ "2, that is 9< km @ 7J km ? DJ km. This is the distancecovered by the ob'ect. To describe distance we need to specify only the numerical value and not the direction of motion. There are certain /uantities which are described by specifying only their numerical values. The numerical value of a physical /uantity is its )agnitude . This difference will give you the numerical value of thedisplacement of the ob'ect from & to 2 through ". The shortest distance measured from the initial to the finalposition of an ob'ect is known as the dis*lace)ent . 2onsider the e-ample given in +%ig. 8 . %or motion of theob'ect from & to ", the distance covered is 9< km and the magnitude of displacement is also 9< km. *uring itsmotion from & to " and back to >, the distance covered ? 9< km @ 5J km ? LJ km while the magnitude of displacement ? 7J km.





Thus, the magnitude of displacement +7J km is not e/ual to the path length +LJ km . %urther, we will notice thatthe magnitude of the displacement for a course of motion may be ero but the corresponding distance covered isnot ero. !f we consider the ob'ect to travel back to &, the final position coincides with the initial position, andtherefore, the displacement is ero. 1owever, the distance covered in this 'ourney is &" @ "& ? 9< km @ 9< km ?85< km. Thus, two different physical /uantities R the distance and the displacement, are used to describe theoverall motion of an ob'ect and to locate its final position with reference to its initial position at a given time.

UNIFORM MOTION AND NON0UNIFORM MOTION

2onsider an ob'ect moving along a straight line. 0et it travel J< km in the first hour, J< km more in the secondhour, J< km in the third hour and J< km in the fourth hour. !n this case, the ob'ect covers J< km in each hour. "sthe ob'ect covers e/ual distances in e/ual intervals of time, it is said to be in uniform motion. The time interval inthis motion may be small or big. !n our dayCtoCday life, we come across motions where ob'ects cover une/ualdistances in e/ual intervals of time, for e-ample, when a car is moving on a crowded street or a person is 'oggingin a park. These are some instances of nonCuniform motion.

Measuring the Rate of Motion

*ifferent ob'ects may take different amounts of time to cover a given distance. ome of them move fast and somemove slowly. The rate at which ob'ects move can be different. "lso, different ob'ects can move at the same rate.&ne of the ways of measuring the rate of motion of an ob'ect is to find out the distance travelled by the ob'ect inunit time. This /uantity is referred to as speed. The ! unit of speed is metre per second. This is represented by thesymbol m s –8 or mNs. The other units of speed include centimetre per second +cm s –8 and kilometre per hour +kmh –8 . To specify the speed of an ob'ect, we re/uire only its magnitude. The speed of an ob'ect need not be constant.!n most cases, ob'ects will be in nonCuniform motion. Therefore, we describe the rate of motion of such ob'ects interms of their average speed. The average speed of an ob'ect is obtained by dividing the total distance travelled by the total time taken. That is,

!f an ob'ect travels a distance s in time t then its speed v is,

0et us understand this by an e-ample. " car travels a distance of 8<< km in 5 h. !ts average speed is J< km h –8. Thecar might not have travelled at J< km h –8 all the time. ometimes it might have travelled faster and sometimesslower than this.

E-ample 8 "n ob'ect travels 89 m in I s and then another 89 m in 5 s. What is the average speed of the ob'ect

olutionTotal distance travelled by the ob'ect ? 89 m @ 89 m ? 75 mTotal time taken ? I s @ 5 s ? 9 s





Therefore, the average speed of the ob'ect is J.77 m s –

S*eed ,ith Direction

The rate of motion of an ob'ect can be more comprehensive if we specify its direction of motion along with itsspeed. The /uantity that specifies both these aspects is called velocity. Pelocity is the speed of an ob'ect moving ina definite direction. The velocity of an ob'ect can be uniform or variable. !t can be changed by changing theob'ectGs speed, direction of motion or both. When an ob'ect is moving along a straight line at a variable speed, wecan e-press the magnitude of its rate of motion in terms of average velocity. !t is calculated in the same way as wecalculate average speed.

!n case the velocity of the ob'ect is changing at a uniform rate, then average velocity is given by the arithmeticmean of initial velocity and final velocity for a given period of time. That is,

where v av is the average velocity, u is the initial velocity and v is the final velocity of the ob'ect.

peed and velocity have the same units, that is, m sC8

or mNs.

E-ample 5 The odometer of a car reads 5<<< km at the start of a trip and 5I<< km at the end of the trip. !f the triptook L h, calculate the average speed of the car in km h C8 and m s C8.

olution*istance covered by the car,s ? 5I<< km – 5<<< km ? I<< kmTime elapsed, t ? L h "verage speed of the car is,





The average speed of the car is J< km h C8 or 87.D m s C8.

E-ample 7 (sha swims in a D< m long pool. he covers 8L< m in one minute by swimming from one end to theother and back along the same straight path. %ind the average speed and average velocity of (sha.

olutionTotal distance covered by (sha in 8 min is 8L< m.*isplacement of (sha in 8 min ? < m

The average speed of (sha is 7 m s C8 and her average velocity is < m s C8.

Rate of Change of "elocity

*uring uniform motion of an ob'ect along a straight line, the velocity remains constant with time. !n this case, thechange in velocity of the ob'ect for any time interval is ero. 1owever, in nonCuniform motion, velocity varies with





time. !t has different values at different instants and at different points of the path. Thus, the change in velocity of the ob'ect during any time interval is not ero.

To e-press the change in velocity of an ob'ect we have to introduce another physical /uantity called acceleration, which is a measure of the change in the velocity of an ob'ect per unit time. That is,

!f the velocity of an ob'ect changes from an initial value u to the final value v in time t, the acceleration a is,

This kind of motion is known as accelerated motion. The acceleration is taken to be positive if it is in the directionof velocity and negative when it is opposite to the direction of velocity. The ! unit of acceleration is m s C5. !f anob'ect travels in a straight line and its velocity increases or decreases by e/ual amounts in e/ual intervals of time,then the acceleration of the ob'ect is said to be uniform. The motion of a freely falling body is an e-ample of uniformly accelerated motion. &n the other hand, an ob'ect can travel with nonCuniform acceleration if its velocity changes at a nonCuniform rate. %or e-ample, if a car travelling along a straight road increases its speed by une/ualamounts in e/ual intervals of time, then the car is said to be moving with nonCuniform acceleration.

E-ample I tarting from a stationary position, Aahul paddles his bicycle to attain a velocity of 9 m s C8 in 7< s. Thenhe applies brakes such that the velocity of the bicycle comes down to I m s C8 in the ne-t J s. 2alculate theacceleration of the bicycle in both the cases.

olution!n the first caseBinitial velocity, u ? < 4final velocity, v ? 9 m s–8 4time, t ? 7< s .%rom E/. +L.7 , we have

ubstituting the given values of u,v and t in the above e/uation, we get

!n the second caseBinitial velocity, u ? 9 m s C84final velocity, v ? I m s C84time, t ? J s.





The acceleration of the bicycle in the first case is <.5 m s C5 and in the second case, it is –<.

&ra*hical Re*resentation of Motion

#raphs provide a convenient method to present basic information about a variety of events. %or e-ample, in thetelecast of a oneCday cricket match, vertical bar graphs show the run rate of a team in each over. "s you have

studied in mathematics, a straight line graph helps in solving a linear e/uation having two variables. To describethe motion of an ob'ect, we can use line graphs. !n this case, line graphs show dependence of one physical/uantity, such as distance or velocity, on another /uantity, such as time.

Distance0Ti)e &ra*hs

The change in the position of an ob'ect with time can be represented on the distanceCtime graph adopting aconvenient scale of choice. !n this graph, time is taken along the -–a-is and distance is taken along the yCa-is.*istanceCtime graphs can be employed under various conditions where ob'ects move with uniform speed, nonCuniform speed, remain at rest etc.

We know that when an ob'ect travels e/ual distances in e/ual intervals of time, it moves with uniform speed. Thisshows that the distance travelled by the ob'ect is directly proportional to time taken. Thus, for uniform speed, a





graph of distance travelled against time is a straight line, as shown in %ig. 7. The portion &> of the graph showsthat the distance is increasing at a uniform rate. 3ote that, you can also use the term uniform velocity in place of uniform speed if you take the magnitude of displacement e/ual to the distance travelled by the ob'ect along the yCa-is.

We can use the distanceCtime graph to determine the speed of an ob'ect. To do so, consider a small part "> of thedistanceCtime graph shown in %ig 7. *raw a line parallel to the -Ca-is from point " and another line parallel to the

yCa-is from point >. These two lines meet each other at point 2 to form a triangle ">2. 3ow, on the graph, "2denotes the time interval +t 5 – t 8 while >2 corresponds to the distance +s 5 – s 8 . We can see from the graph that asthe ob'ect moves from the point " to >, it covers a distance +s 5 – s 8 in time +t 5 – t 8 . The speed, v of the ob'ect,therefore can be represented as

We can also plot the distanceCtime graph for accelerated motion. Table shows the distance travelled by a car in atime interval of two seconds.

The distanceCtime graph for the motion of the car is shown in %ig. I. 3ote that the shape of this graph is differentfrom the earlier distanceCtime graph +%ig. 7 for uniform motion. The nature of this graph shows nonlinear variation of the distance travelled by the car with time. Thus, the graph shown in %ig I represents motion withnonCuniform speed.





&ra*hical Re*resentation of Motion "elocity0Ti)e &ra*hs

The variation in velocity with time for an ob'ect moving in a straight line can be represented by a velocityCtimegraph. !n this graph, time is represented along the -Ca-is and the velocity is represented along the yCa-is. !f theob'ect moves at uniform velocity, the height of its velocityCtime graph will not change with time +%ig. J . !t will bea straight line parallel to the -Ca-is. %ig. J shows the velocityCtime graph for a car moving with uniform velocity of I< km h C8.

We know that the product of velocity and time give displacement of an ob'ect moving with uniform velocity. Thearea enclosed by velocityCtime graph and the time a-is will be e/ual to the magnitude of the displacement. To





know the distance moved by the car between time t 8 and t 5 using %ig. J, draw perpendiculars from the pointscorresponding to the time t 8 and t 5 on the graph. The velocity of I< km h C8 is represented by the height "2 or >*and the time +t 5 – t 8 is represented by the length ">.

o, the distance s moved by the car in time +t 5 – t 8 can be e-pressed ass ? "2 S 2* ? K+I< km h C8 S +t5 – t 8 h

? I< +t 5– t 8 km ? area of the rectangle ">*2 +shaded in %ig. J .

We can also study about uniformly accelerated motion by plotting its velocity– time graph. 2onsider a car beingdriven along a straight road for testing its engine. uppose a person sitting ne-t to the driver records its velocity after every J seconds by noting the reading of the speedometer of the car. The velocity of the car, in km h C8 as wellas in m s C8, at different instants of time is shown in table.

!n this case, the velocityCtime graph for the motion of the car is shown in %ig. 9. The nature of the graph showsthat velocity changes by e/ual amounts in e/ual intervals of time. Thus, for all uniformly accelerated motion, the

velocityCtime graph is a straight line.





We can also determine the distance moved by the car from its velocityCtime graph. The area under the velocityCtime graph gives the distance +magnitude of displacement moved by the car in a given interval of time. !f the car would have been moving with uniform velocity, the distance travelled by it would be represented by the area ">2* under the graph +%ig. 9 . ince the magnitude of the velocity of the car is changing due to acceleration, thedistance s travelled by the car will be given by the area ">2*E under the velocityCtime graph +%ig. 9 . That is,s ? area ">2*E ? area of the rectangle ">2* @ area of the triangle "*E ? "> S >2 @ +"* S *E

!n the case of nonCuniformly accelerated motion, velocityCtime graphs can have any shape.

%ig. 6+a shows a velocityCtime graph that represents the motion of an ob'ect whose velocity is decreasing withtime while %ig. 6 +b shows the velocityCtime graph representing the nonCuniform variation of velocity of the ob'ect with time. Try to interpret these graphs.

E9uations of Motion +y &ra*hical Method





When an ob'ect moves along a straight line with uniform acceleration, it is possible to relate its velocity,acceleration during motion and the distance covered by it in a certain time interval by a set of e/uations known asthe e/uations of motion. There are three such e/uations. These areB

Where u is the initial velocity of the ob'ect which moves with uniform acceleration a for time t, v is the final velocity, and s is the distance travelled by the ob'ect in time t. E/. +J describes the velocityCtime relation and E/.+9 represents the positionCtime relation. E/. +6 , which represents the relation between the position and the velocity, can be obtained from E/s. +J and +9 by eliminating t. These three e/uations can be derived by graphicalmethod.

E9uation for "elocity0Ti)e Relation

2onsider the velocityCtime graph of an ob'ect that moves under uniform acceleration as shown in %ig. L +similar to%ig. 9, but now with u U < . %rom this graph, you can see that initial velocity of the ob'ect is u +at point " and thenit increases to v +at point > in time t. The velocity changes at a uniform rate a. !n %ig. L, the perpendicular lines>2 and >E are drawn from point > on the time and the velocity a-es respectively, so that the initial velocity isrepresented by &", the final velocity is represented by >2 and the time interval t is represented by &2. >* ? >2 –2*, represents the change in velocity in time interval t.

0et us draw "* parallel to &2. %rom the graph, we observe that>2 ? >* @ *2 ? >* @ &"





ubstituting >2 ? v and &" ? u,

We getv ? >* @ u&r>* ? v – u+L%rom the velocityCtime graph +%ig. L , the acceleration of the ob'ect is given by

ubstituting &2 ? t, we geta ? >*Nt&r>* ? at+D(sing E/s. +L and +D we get v ? u @ at

E9uation for Position0Ti)e Relation

0et us consider that the ob'ect has travelled a distance s in time t under uniform acceleration a. !n %ig. L, thedistance travelled by the ob'ect is obtained by the area enclosed within &">2 under the velocityCtime graph ">.Thus, the distance s travelled by the ob'ect is given by

s ? area &">2 +which is a trape ium ? area of the rectangle &"*2 @ area of the triangle ">* ? &" S &2 @ 8N5 +"* S >* +8<

ubstituting &" ? u, &2 ? "* ? t and >* ? at, we get

s ? u S t @ 8N5+t S ators ? u t @ 8N5 a t 5

E9uation for Position0"elocity Relation

%rom the velocityCtime graph shown in %ig. L, the distance s travelled by the ob'ect in time t, moving underuniform acceleration a is given by the area enclosed within the trape ium &">2 under the graph. That is,

ubstituting &" ? u, >2 ? v and &2 ? t, we get





%rom the velocityCtime relation +E/. 9 , we get

(sing E/s. +88 and +85 we have

E3a)*le < " train starting from rest attains a velocity of 65 km h C8 in J minutes. "ssuming that the accelerationis uniform, find +i the acceleration and +ii the distance travelled by the train for attaining this velocity.

Solution We have been givenu ? < 4 v ? 65 km h C8 ? 5< m sC8 and t ? J minutes ? 7<< s.+i %rom E/. +J we know that

+ii %rom E/. +6 we have5as ? v 5 – u 5 ? v 5 – <Thus,

The acceleration of the train is and the distance travelled is 7 km.





E3a)*le = " car accelerates uniformly from 8L km h C8 to 79 km h C8 in J s. 2alculate +i the acceleration and +iithe distance covered by the car in that time.

Solution We are given thatu ? 8L km h C8 ? J m s C

v ? 79 km h C8 ? 8< m s C8 and

t ? J s .+i %rom E/. +J we have

+ii %rom E/. +9 we have

s ? u t @ at? J m s C8 S J s @ 8N5 S 8 m s C5 S +Js? 5J m @ 85.J m? 76.J mThe acceleration of the car is 8 m s C5 and the distance covered is 76.J m.

E3a)*le > The brakes applied to a car produce an acceleration of 9 m s C5 in the opposite direction to the motion.!f the car takes 5 s to stop after the application of brakes, calculate the distance it travels during this time.

Solution We have been given

a ? – 9 m sC5

4 t ? 5 s and v ? < m sC8

%rom E/. +J we know that v ? u @ at< ? u @ +– 9 m s C5 S 5 s&ru ? 85 m s C8 %rom E/. +9 we gets ? u t @ a t? +85 m s C8 S +5 s @ +–9 m s C5 +5 s? 5I m – 85 m? 85 mThus, the car will move 85 m before it stops after the application of brakes

Unifor) Circular Motion

When the velocity of an ob'ect changes, we say that the ob'ect is accelerating. The change in the velocity could bedue to change in its magnitude or the direction of the motion or both.





0et us consider an e-ample of the motion of a body along a closed path. %ig D +a shows the path of an athletealong a rectangular track ">2*. 0et us assume that the athlete runs at a uniform speed on the straight parts ">,>2, 2* and *" of the track. !n order to keep himself on track, he /uickly changes his speed at the corners. !t isclear that to move in a rectangular track once, the athlete has to change his direction of motion four times.

3ow, suppose instead of a rectangular track, the athlete is running along a he-agonal shaped path ">2*E%, asshown in %ig. D+b . !n this situation, the athlete will have to change his direction si- times while he completes oneround. !t is observed that as the number of sides of the track increases the athelete has to take turns more and

more often. !f we go on increasing the number of sides indefinitely, we will notice that the shape of the track approaches the shape of a circle and the length of each of the sides will decrease to a point. !f the athlete moves with a velocity of constant magnitude along the circular path, the only change in his velocity is due to the changein the direction of motion. The motion of the athlete moving along a circular path is, therefore, an e-ample of anaccelerated motion.

We know that the circumference of a circle of radius r is given by 5Vr. !f the athlete takes t seconds to go oncearound the circular path of radius r, the velocity v is given by

When an ob'ect moves in a circular path with uniform speed, its motion is called uniform circular motion.

When an athlete throws a hammer or a discus in a sports meet, heNshe holds the hammer or the discus in hisNherhand and gives it a circular motion by rotating hisNher own body. &nce released in the desired direction, thehammer or discus moves in the direction in which it was moving at the time it was released 'ust like the piece of


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