Chapter 3- Linear Motion

Speed, velocity and accelerationSpeed, velocity and acceleration

Displacement vs. Distance

Distance – Scalar: How far did I travelDistance – Scalar: How far did I travel?? Example: 60 kmExample: 60 km

Displacement – Vector: How far am I and in Displacement – Vector: How far am I and in what direction from where I started?what direction from where I started?

Example: 60 km NorthExample: 60 km North

Speed

Average SpeedAverage Speed =Total distance traveled =Total distance traveled divided by the time of travel. speed = divided by the time of travel. speed = distance/time: distance/time: Units?Units?

km/h or mph (really mi/h is better) km/h or mph (really mi/h is better) meters/second (m/s)meters/second (m/s)

62mph is aprox. 100 km/h or about 62mph is aprox. 100 km/h or about 28 m/s28 m/s

• i.e. 1 m/s = 2 mph (approximately)i.e. 1 m/s = 2 mph (approximately)

t

dv

Speed

Instantaneous speedInstantaneous speed What we normally call speedWhat we normally call speed How fast an object is moving at any How fast an object is moving at any

given instant.given instant. This is what we read on the speedometer This is what we read on the speedometer

of a car.of a car.

Average Speed and Distance

Ave. speed = total distance/time of travelAve. speed = total distance/time of travel

Note: During a trip, you may never be going at Note: During a trip, you may never be going at your average speed for very long.your average speed for very long.

How far am I going?How far am I going? Distance = Ave. speed x time Distance = Ave. speed x time Check unitsCheck units

compare with Ave. speedcompare with Ave. speed

tvd

t

dv

Velocity It’s a vector! Displacement ÷ time It’s a vector! Displacement ÷ time

Example: 50 km/hr NorthExample: 50 km/hr North Instantaneous - your speed and your direction of Instantaneous - your speed and your direction of

motion at a particular instant.(Word often omitted)motion at a particular instant.(Word often omitted) Example: 100 km/h SouthExample: 100 km/h South

So…speed is the magnitude of velocity!So…speed is the magnitude of velocity! Constant Velocity – constant speed in a straight Constant Velocity – constant speed in a straight

lineline Changing velocity means going faster, slower Changing velocity means going faster, slower

and/or changing direction.and/or changing direction. Whenever speed and/or direction changes Whenever speed and/or direction changes

(changing velocity) an object is accelerating.(changing velocity) an object is accelerating.

t

dv

Fig.3.3

Fig. 3.4

Concept QuestionJack is riding a bike from Fayetteville to Springdale at 12 m/h. Jack is riding a bike from Fayetteville to Springdale at 12 m/h.

Jill is riding a bike back from Springdale to Fayetteville at 12 Jill is riding a bike back from Springdale to Fayetteville at 12 m/h. As they pass each other.m/h. As they pass each other.a. their speeds are identical and their velocities area. their speeds are identical and their velocities are

identical.identical.b. their speeds are different and their velocities are b. their speeds are different and their velocities are different.different.c. their speeds are different and their velocities are c. their speeds are different and their velocities are identical.identical.d. their speeds are identical and their velocities are d. their speeds are identical and their velocities are different.different.e. theoretical physics predicts they will turn into giant e. theoretical physics predicts they will turn into giant frogs.frogs.

Acceleration

Acceleration is a measure of "how quickly ‘how fast’ Acceleration is a measure of "how quickly ‘how fast’ Changes". We can feel it, but we can’t see it!Changes". We can feel it, but we can’t see it!

Acceleration is Acceleration is changechange in velocity with time – a vector in velocity with time – a vector quantityquantity Speeds up, slows down, changes directionSpeeds up, slows down, changes direction When an object has a constant velocity it has When an object has a constant velocity it has nono

acceleration.acceleration.

Revisit Newton’s 1Revisit Newton’s 1stst Law: Law: An object will not accelerate unless a net force acts on it An object will not accelerate unless a net force acts on it (the acceleration is in the same direction as the net force)(the acceleration is in the same direction as the net force)

Acceleration (cont.)When an object is in equilibrium:When an object is in equilibrium:

Its velocity is constant.Its velocity is constant. Its acceleration is 0.Its acceleration is 0. The net force acting on it is 0.The net force acting on it is 0.

Average acceleration tells on average how quickly Average acceleration tells on average how quickly the velocity the velocity changeschanges over a period of time. over a period of time.

Instantaneous Acceleration – how quickly the Instantaneous Acceleration – how quickly the velocity is changing in an instant of timevelocity is changing in an instant of time

t

va

Acceleration (cont.)

Standard UnitsStandard Units British EngineeringBritish Engineering

Miles per hour per second: mi/hr/sMiles per hour per second: mi/hr/sFeet per second/per second: ft/s/s (ft/sFeet per second/per second: ft/s/s (ft/s22))

MetricMetric Kilometers per hour per second: km/hr/sKilometers per hour per second: km/hr/s Meters/second/second: m/s/s (m/sMeters/second/second: m/s/s (m/s22))

Common UsageCommon Usage Acceleration – Speeding upAcceleration – Speeding up Deceleration – Slowing downDeceleration – Slowing down

Concept Questions

Q. A car drives 50 mi/hr in a straight line for 5 s. What is Q. A car drives 50 mi/hr in a straight line for 5 s. What is its acceleration?its acceleration?

Q. Car Q. Car AA accelerates from 50 mph to 60 mph. Car accelerates from 50 mph to 60 mph. Car BB accelerates from 30 mi/hr to 40 mi/hr. Which has the accelerates from 30 mi/hr to 40 mi/hr. Which has the greater acceleration?greater acceleration?

Describe the Motion

Free Fall Objects falling near the earth’s surface under the Objects falling near the earth’s surface under the

influence of gravity only (no air friction).influence of gravity only (no air friction). The acceleration of all objects is The acceleration of all objects is 9.8 m/s/s9.8 m/s/s (32 (32

ft/s/s) or about ft/s/s) or about 10 m/s/s10 m/s/s. . We use We use “g”“g” as the symbol for the acceleration due as the symbol for the acceleration due

to gravity.to gravity. How fast 1 s after drop? 2 s?How fast 1 s after drop? 2 s? If an object falls from rest, then its instantaneous If an object falls from rest, then its instantaneous

velocity is just acceleration (g) • timevelocity is just acceleration (g) • time

Velocity change is constantVelocity change is constant

gtv

How Fast ?

Fig. 3.7

An object projected straight up has constant acceleration after it leaves the projector Direction signDirection sign

Up – PositiveUp – Positive Down – NegativeDown – Negative

Fig. 3.8

Distance (How far) in Free Fall(Constant Acceleration)

Again, assume we start from rest. How far in 1 s?Again, assume we start from rest. How far in 1 s? Distance is the Distance is the AverageAverage velocity x time of fall. velocity x time of fall.

For constant accelerationFor constant acceleration

When vWhen vii = 0, then = 0, then 2

2

1gtd

tvd

2fi

vvv

Now Far ?

Fig. 3.9

Check (Challenge) Question: Consider a rifle fired straight downward from a high-Consider a rifle fired straight downward from a high-

altitude balloon. If the muzzle velocity is 100 m/s and air altitude balloon. If the muzzle velocity is 100 m/s and air resistance can be neglected:resistance can be neglected:

What is the What is the acceleration acceleration of the bullet after one second?of the bullet after one second? What is the speed of the bullet after one second?What is the speed of the bullet after one second?

How far has the bullet gone after one second?How far has the bullet gone after one second?

gtvvif

2

2

1gttvd

i

Figure 3.10

Fig. 3.10

YouTube - Feather & Hammer Drop on Moon