kinematics. lesson structure part 1 – instantaneous speed vs average speed – scalars vs vectors...

Kinematics

Introduction

• Kinematics is the study of moving objects• In the previous lesson you have been

introduced to physical quantities, and studied 4 of them

• In this topic, we will be investigating how 6 quantities interact with each other in moving objects:

• distance, displacement, speed, velocity, time, acceleration

Speed

• Speed is the measure of how fast or how slow an object moves

• Units: ms-1, kmh-1

• Previously, you’ve learned that speed = distance / time

• Is this the only way to understand speed?

The fastest man on Earth

• Usain Bolt’s fastest time for the 100 m race is 9.58 s (2009 IAAF Championships in Berlin)

• What was his speed?• Speed = distance/time• 100/ 9.572 = 10.4 ms-1

• “Usain Bolt is the fastest man on Earth (ever), so it is not humanly possible to go faster than 10.4 ms-1. “

• Do you agree with this statement?

The fastest man on Earth

• Look at the breakdown of Bolt’s run:

• Usain Bolt actually reached a top speed of 12.4 ms-1, faster than the 10.4 ms-1 we mentioned previously!

Time /s Speed/ms-1

0 to 20 m 2.89 6.92

20 to 40 m 1.75 11.4

40 to 60 m 1.67 12.0

60 to 80 m 1.61 12.4

80 to 100 m 1.66 12.0

Total 9.58 10.4

Instanteous Speed vs Average Speed

• There are two different ways to talk about speed: instantaneous speed or average speed

• Instantanous speed is how fast an object is moving at that instant in time

• Average Speed is given by the formula• Avg Speed = Total Distance / Total Time

Instanteous Speed vs Average Speed

• Traffic police catching speeding vehicles: are they interested in instantaneous speed or average speed?

• How do they measure this?• The toll booth in the Malaysian highway

charges you for speeding if you take too short a time to travel from place A to place B. Are they measuring instantaneous speed or average speed?

• How can you avoid being charged?

Practice Task

Distance vs Displacement• If I walked 3 metres to the front and then 6 metres

to the back:• How far have I travelled?• This is an ambigious question. There are two ways of

interpreting this question:• 1) How much total distance have I travelled?• 2) How much distance is there between my current

position and my starting position?• The first is asking for the quantity “distance”• The second is asking for the quantity “displacement”

Displacement

• Symbol for displacement is “s”• Units: m• Question: is it possible to have negative

displacement?• How about distance?• Direction matters for displacment, but doesn’t

matter for distance!• Note: in this topic we are generally concerned about

motion in a straight line (one-dimensional motion)

Speed vs Velocity

• You may have come across the term “velocity” and you may have used it interchangeably with “speed”

• In Physics they are actually different (but related) quantities

• The difference between speed and velocity is the same difference between distance and displacement

Speed vs Velocity

• Direction matters for velocity but does not matter for speed

• The sign convention for velocity follows the sign convention for displacement

• E.g. if moving to the right is positive displacement, moving to the right is positive velocity as well

Speed vs Velocity

• Official definition (to be memorized)• Speed is the distance moved per unit time• Velocity is the rate of change of displacement

Scalars vs Vectors• Quantities which have direction as well as

magnitude are known as vectors• Quantities which only have magnitude are

known as scalars• This is the list of scalars and vectors which you

have studied so far:Scalars Vectors

Mass Force (e.g. Weight)

Distance Displacement

Speed Velocity

Acceleration

• In English, we use the term “acceleration” to describe an object which is going faster and faster (as opposed to constant speed)

• If an object is going slower and slower, does it have acceleration?

• Yes!!• As long as an object has changing velocity, it

has an acceleration• Definition: the rate of change of velocity

Acceleration

• Question: A car is making a right turn at constant speed. Does it have an acceleration?

• Yes!• The direction of the car changed, hence the

velocity of the car changed (recall that velocity is a vector). Thus there is a acceleration.

Uniform Acceleration (straight line)• When an object is changing its velocity at a

constant rate, it is said to have uniform acceleration

• Definition: a constant rate of change of velocity

Uniform Acceleration

• The following equation applies (only) if acceleration is uniform:

• a = (v-u)/t– a = acceleration– u = initial velocity– v = final velocity– t = time

• From this equation, can you determine units of acceleration?

Deceleration

• You may come across the term “deceleration”, referring to an object going slower and slower.

• Deceleration is actually negative acceleration• Uniform deceleration is when an object is

going slower and slower at a constant rate.• In uniform deceleration cases, you may still

use the equation a = (v-u)/t, but acceleration must be a negative value

Practice Task

Important!• Presentation of Working in Calculation

Questions

• Step 1: Equation Step• Step 2: Substitution Step• Step 3: Intermediate Answers calculate to at

least 4 s.f.• Step 4: Final Answers provide to 3 s.f, with

correct units

Quiz 2A

Assignment 2A

• TYS Topic 2• Paper 1: Qn 1, 3, 5, 8, 12

• Due Date:• Reminder: Late Work Policy

Finding Gradient

• Recall from Maths:• Gradient = Rise/Run

• Practice Task

Kinematics Graphs

• Often in kinematics, we use graphs to describe the motion of objects, since graphs can provide a lot of information while taking less space

• You need to be familiar two kinds of graphs:• 1) Displacement – Time Graphs• 2) Velocity – Time Graphs

Displacement-Time Graph

• In an s-t graph, the vertical axis represents displacement (s) while the horizontal axis represents time (t)

• Reading an s-t graph helps us to find• a) the displacement of an object at any one

time• b) the velocity of an object at any one time

s-t graph (uniform velocity)

• Can you describe the graph below?• What is the velocity when t = 10 s?

s/m

t/s 2 4 6 8 10 12

100

60

40

20

0

80

Practice Task

Characteristics of s-t graph (uniform velocity)

• Straight line• gradient is the same at any point on the

straight line• the gradient represents velocity• What is happening if the s-t graph shows a flat

line?• What is happening if the s-t graph shows a line

which is sloping downwards?

s-t graph (non-uniform velocity)

• Can you describe the velocity of this object?

• gradient is increasing = velocity is increasing

s/m

t/s 2 4 6 8 10 12 14 16 18 20

10080

604020

0

s-t graph (non-uniform velocity)

• Can you describe the velocity of this object?

• gradient is decreasing = velocity is decreasing

s/m

t/s 2 4 6 8 10 12 14 16 18 20

10080

604020

0

Characteristics of s-t graph (non-uniform velocity)

• curve• Find gradient by taking the tangent of the

curve• gradient represents instantaneous velocity• gradient changing with time = velocity

changing with time• increasing gradient = increasing velocity• decreasing gradient = decreasing velocity

Practice Task

Quiz 2B

Assignment 2B

• TYS Topic 2• Paper 2 Qn 1 [handout]

Velocity-Time Graph

• In a v-t graph, the vertical axis represents velocity while the horizontal axis represents time

• Reading a v-t graph can help us to find:• 1) instantaneous velocity at any one point in time• 2) instantaneous acceleration at any one point in

time• 3) displacement covered in a time interval

(between two points in time)

v-t graph (uniform acceleration)• Gradient of v-t graph = acceleration• What is the acceleration of this object?v/m s-1

0 2 4 6 8 10 12 13 14t/s

5

15

20 10

30 25

35

0

Characteristics of v-t graph (uniform acceleration)

• Straight line graph• Gradient is constant = acceleration is constant• What would a v-t graph of an object with

constant velocity look like?• What would a v-t graph of an object at rest

look like?• What would a v-t graph of an object with

uniform decreasing velocity look like?

v-t Graph (non-uniform acceleration)

• Can you describe this graph?

• gradient is decreasing = acceleration is decreasing

1 2 3 4 5 6 7 8 9 10 11 12

v/m s-1

t/s

0

20

10

30

Characteristics of v-t graph (non-uniform acceleration)

• curve• gradient represents instantaneous

acceleration• gradient changing with time = acceleration

changing with time• increasing gradient = increasing acceleration• decreasing gradient = decreasing acceleration

Practice Task

• Task 1: GLM pg 37 Qn 2(b)(i)-(iv)

• Task 2: GLM pg 38 Qn 4(a)(i)-(ii)

finding displacement from v-t graphs

• Unlike s-t graphs, there is one more way to gain information from v-t graphs (aside from finding gradient)

• The area under a time interval v-t graph shows the displacement covered by that time interval

finding displacement from v-t graphs

• Find displacement covered:• a) t = 0 s to t = 3 s• b) t = 3 s to t = 7.5 s• c) t = 7.5 s to t = 12 s• d) in total?

t/s

v/m s-1

0 1 2 3 4 5 6 7 8 9 10 11 12

10

20

30

40

50

Practice Task

• Task 1: GLM pg 38 Qn 4(b)-(c)

• Task 2: GLM pg 45 Qn 7-8

Drawing your own v-t graph

• Sometimes a graph may not be provided, but you may be required to sketch your own v-t graph to solve the question.

Practice Task

• Task 1: GLM pg 42, Qn 1, 3

• Task 2: GLM pg 33, Qn 3 (actual question)

Quiz 2C

Putting it all together

• Most numerical problems involve 4 of these 5 quantities: v, u, a, s, t

auvts

If question involves these 4 quantities, use a = (v-u)/t to solve

If question involves these 4 quantities, draw your own v-t graph to solve

Putting it all together

s-t graph v-t graphread off the

graphdisplacement velocity

gradient velocity accelerationarea under - displacement

Putting it all together

Velocity

Acceleration

Displacement

gradient (differentiate)

gradient (differentiate) area under (integrate)

Assignment 2C

• TYS Topic 2• Paper 1: Qn 5, 7, 9• Paper 2: Qn 4, 6

Summary• instantaneous vs average speed• scalars vs vectors• a = (v-u)/t• s-t graphs– finding velocity

• v-t graphs– finding acceleration– finding displacement– drawing own v-t graph