1. Chapter 2 Kinematics Slide 1 of 24
Everything in the universe is in motion.
Nothing is permanently at rest.
Kinematics
These slides adapted from materials from Longman
~ Ismail Brian Wee, 2009 ~
Slide 1 of 24

2. Contents Speed, Velocity and Acceleration Graphical Analysis of Motion
Free-fall
Chapter Review
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3. Speed
Speed, v
Speed of an object is defined as the distance travelled per unit time.
SI unit of metres per second (ms-1)
speed (ms-1) =
time taken (s)
distance travelled (m)
* Note: Remember to USE THE CORRECT UNITS
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4. Speed
Average Speed, v
Average speed of an object is defined as the total distance travelled divided by the total time taken.
has a unit of metres per second (ms-1)
average speed (ms-1) =
total time (s)
total distance (m)
* Note: Remember to USE THE CORRECT UNITS
for most journeys, speed is not constant
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5. Speed Instantaneous Speed
Instantaneous speed is the speed of an object at any instant
(any point in time).
A speedometer measures the instantaneous speed of the car
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6. Speed, Velocity and Acceleration
Velocity, v
Velocity is the displacement per unit time in a stated direction; or speed in a specified direction.
has a unit of metres per second (ms-1)
Velocity (ms-1) =
time (s)
displacement (m)
* Note: Remember to USE THE CORRECT UNITS
Slide 6 of 24

7. Speed and Velocity Difference between Speed & Velocity
scalar quantity
vector quantity
regardless of its direction
dependent on direction of motion
A negative velocity indicates that a body is moving in the opposite direction to the direction stated.
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8. Velocity Velocity Consider a vehicle travelling around a bend.
At a road bend, although the vehicle’s speed is constant, its velocity is continuously changing (because direction is constantly changing)
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9. Acceleration v – u a = t Acceleration
Acceleration is defined as the rate of change of velocity.
has a unit of metres per second square (ms-2)
Acceleration (ms-2) =
time taken for the change (s)
change of velocity (ms-1)
* Note: Remember to USE THE CORRECT UNITS
this formula is often used, where
v  Final Velocity (ms-1)
u  Initial Velocity (ms-1)
t  Time taken (s)
a = t
v – u
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10. Acceleration Acceleration
Uniform acceleration occurs when the velocity increases (or decreases) by the same amount per unit time.
[Or rate of change of velocity is constant/uniform]
No acceleration
(acceleration = 0)
Accelerating (positive acceleration)
Decelerating (negative acceleration)
velocity of the moving object is constant throughout
velocity is increasing
velocity is decreasing
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11. A B Graphical analysis of motion Distance Displacement Displacement
Distance is the actual or total length travelled by an object in motion.
Displacement
Displacement is the distance measured along a straight line in a stated direction. A B
Displacement
Distance
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12. Graphical analysis of motion
Displacement-time graphs
Gradient of the displacement-time graph gives the velocity of the object.
Displacement / m
Displacement / m
faster
object is not moving
slower
Time / s
Time / s
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13. object is moving with constant velocity
Graphical analysis of motion
Displacement-time graphs
The displacement-time graph of an object travelling with constant velocity is always a straight line.
In a displacement-time graph, the GRADIENT shows the VELOCITY.
Thus,
Steeper gradient
 Higher Velocity (faster)
Shallower gradient
 Lower Velocity (slower)
Displacement / m
faster
slower
Time / s
object is moving with constant velocity
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14. Graphical analysis of motion
Displacement-time graphs
Time taken, t/s 10 20 30 40 50 60 70
Distance, x/m
100
200
350
550
850
1200
The instantaneous speed of the car at a particular time can be obtained by finding the slope of the tangent to the graph (gradient) at that point in time.
In each successive time interval, 0-10 s, s, and so on, the car covers a greater distance than in the previous one. This means the car is going faster.
550
Slide 14 of 24

15. object has variable velocity
Graphical analysis of motion
Displacement-time graphs
Gradient of a tangent to the displacement-time graph of an object travelling with non-uniform velocity gives its instantaneous velocity at a given time.
Displacement / m
Displacement / m
increasing velocity
decreasing velocity
Time / s
Time / s
object has variable velocity
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16. object moves with constant velocity
Graphical analysis of motion
Velocity-time graphs
Gradient of the velocity-time graph gives the acceleration of a moving body.
Velocity / ms-1
Velocity / ms-1
object moves with constant velocity
object is not moving
Time / s
Time / s
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17. Graphical analysis of motion
Velocity-time graphs
Gradient of the velocity-time graph gives the acceleration of a moving body.
Velocity / ms-1
Velocity / ms-1
acceleration
deceleration
Time / s
Time / s
object has constant acceleration
object has constant deceleration
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18. Graphical analysis of motion
Variable acceleration
Gradient of the velocity-time graph gives the acceleration of a moving body.
Velocity / ms-1
Velocity / ms-1
increasing acceleration
decreasing acceleration
Time / s
Time / s
object has variable acceleration/deceleration
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19. Graphical analysis of motion
Variable acceleration
Not all objects move with constant acceleration. Most vehicles move with accelerations that keep changing.
The acceleration or deceleration of the object at any point in time is still given by the gradient of the graph at that point.
velocity/m s-1
stop
stop
time/s
velocity-time graph of a car on a straight road where it has to stop twice because of traffic lights
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20. graphical analysis of motion
area under a velocity-time graph
The area under the velocity-time graph gives the distance travelled by the moving object.
Velocity / ms-1
In this example,
Distance travelled
= area under graph
(use square formula)
= v t1
uniform velocity v
Time / s t1
Slide 20 of 24

21. Graphical analysis of motion
Area under a velocity-time graph
The area under the velocity-time graph gives the distance travelled by the moving object.
Velocity / ms-1
In this example,
Distance travelled
= area under graph
(use triangle formula)
= ½ v t1 v
uniform acceleration
Time / s t1
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22. Graphical analysis of motion
Area under a velocity-time graph
The area under the velocity-time graph gives the distance travelled by the moving object.
Velocity / ms-1
In this example,
uniform velocity
Distance travelled
= area under graph
(use trapezium formula)
= ½ ( t1 + t2) v v
uniform deceleration
Time / s t1 t2
* Note: You can also find the area by adding the
area of the square and the area of the
triangle
Area of trapezium = ½ x (a + b) x height
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23. Free fall Acceleration due to gravity
All objects fall freely towards the centre of the earth and have the same acceleration (acceleration of free fall).
all objects fall freely at g  10 ms-2 ( if air resistance is negligible )
speed of a free-falling body increases by 10 ms-1 every second or when a body is thrown up
speed of a free-falling body decreases by 10 ms-1 every second or when a body is thrown up
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24. Area under velocity-time graph Displacement-time graph represents
can be plotted as
Area under velocity-time graph
Displacement-time graph
represents
Distance
Displacement
is used to find
gives
provides
can be plotted as
represents
distance
time
speed =
Gradient of displacement-time graph
Velocity-time graph
displacement
time
velocity =
average speed =
total distance
total time
is used to find
provides
represents
Gradient of velocity-time graph
acceleration =
change in velocity
time
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