Topic 2: Mechanics
2.1 Kinematics
B
Displacement is a vector joining the initial position to the final position of an object.
⃗ =
𝒗
Velocity is the rate of change of displacement.
⃗ =
𝒂
Acceleration is the rate of change of velocity.
∆𝒔⃗
A
(Speed is the scalar value of velocity.)
∆𝑡
⃗ displacement
𝒔
⃗ velocity
𝒗
⃗ acceleration
𝒂
⃗
∆𝒗
∆𝑡
𝒔 distance
𝒗 speed
𝒂 acceleration
𝑚
𝑚𝑠 −1
𝑚𝑠 −2
Explain the difference between instantaneous and average speed, velocity and acceleration.
Q1.
Q2.
Q3.
A correct definition of displacement is the distance …
A.
from a fixed point
B.
C.
from a fixed point in a given direction
D.
moved from a fixed point
moved in a given direction
Which of the following statements is false?
A.
The instantaneous speed of an object is never negative.
B.
The average speed of an object is never negative.
C.
If an object has zero instantaneous velocity it must have zero instantaneous acceleration.
D.
If an object returns to its starting point its average velocity for the journey was zero.
Samantha walks along a horizontal path in the direction shown.
The curved part of the path is a semi-circle.
The magnitude of her displacement from point P to point Q is approximately
A.
2 m.
B.
4 m.
C.
6 m.
D.
8 m.
The equations of uniformly accelerated motion (Kinematic equations).
Outline the conditions under which the equations for uniformly accelerated motion may be applied.
(i)
Straight line motion
(ii)
Constant acceleration
Note: The acceleration of a body falling in a vacuum near the Earth’s surface is CONSTANT.
Q4.
The kinematic equations can always be applied when an object is …
I.
describing uniform circular motion
II. falling through water
A.
I only
B.
II only
C.
both
D.
neither
Q5.
An object accelerates from 5 ms-1 to 15 ms-1 in 10 seconds. Assuming the force is constant and in the direction of
2
2
2
2
the motion, the acceleration is
A. 0.5 ms
B. 0.1 ms C. 5 ms D. 1 ms
Q6.
A cat falls out of a 4.9 m tall tree. At what speed does it hit the ground ?
Q7.
Two cars accelerate from rest at 2 ms and 3 ms
How far apart are they after 10 seconds ?
Q8.
2


respectively.
A. 10 m
1

2.0 ms
1
9.8 ms
B.
1.0 s
C.
1.5 s
D.

B.
D.
B. 30 m C. 40 m

A steel ball is released into a bucket of oil. (The oil has a depth of 25 cm). 
ms 2 the time
 it takes to reach the bottom of the bucket is
If the ball accelerates at 0.5
A. 0.5 s
Q9.
2
A.
C.


1
4. 9 ms
1
14.7 ms
D. 50 m
2.5 s
If a salmon swims 
straight upward in the water fast enough to break through the surface
1
at a speed of 6.0 ms , how high can it jump above the water ? A. 1.0 m B. 1.2 m C. 1.4 m D. 1.8 m

"Throw a ball straight up into the air..." (ignoring air resistance)
Q10. You throw a ball straight up into the air, and catch it at the same height on its way down.
A.
Its speed remains constant the entire time of flight.
B.
Its acceleration decreases on the way up, and increases on the way down
C.
The ball's velocity at the instant it is thrown is the same as when it is caught.
D.
The speed of the ball is the same at the instant it is thrown as when it is caught.
Q11.
A person at the top of a high building throws a ball vertically upwards with an initial velocity
of 20 ms-1. The time taken by the ball to return to the person is
A.
about 1 s
B.
about 2 s
C.
about 3 s
D.
about 4 s
Q12.
A stone is thrown vertically upwards, and then returns to the ground.
At the top of its path its acceleration is
A. zero
B. upwards
C. downwards D. changing direction from up to down
Q13.
A ball is thrown straight up into the air at 15 𝑚𝑠 −1 .
How long does it take the ball to reach its greatest height ?
Q14.
A ball thrown vertically upwards lands 6 seconds later.
How high does the ball reach? (use g = 10 m𝑠 −2 )
A. 25m
B. 36 m
C.
A ball is thrown straight up at 8 ms-1. How high is the ball
when it is travelling at 4 ms-1 ? (use g = 10 m𝑠 −2 )
A. 1.4 m
B. 2.4 m
C. 3.4 m
Q15.
A.
C.
15g s
7.5g s
B. 15/g s
D. 7.5/g s
45 m
D. 60 m
D. 4.4 m
20 𝑚𝑠 −1
A ball is thrown straight up at 20 𝑚𝑠 −1 from the edge of a 40 𝑚 high cliff.
(a) How high does the ball reach? (use g = 10 m𝑠 −2 )
(b) How fast is the ball travelling as it passes the boy on the way down?
40 𝑚
(c) Where is the ball travelling at 5 𝑚𝑠 −1 ?
(d) When does the ball strike the water?
(e) When is the ball travelling at 35 𝑚𝑠 −1 ?
"A ball freefalls 60 m in the last 2 seconds of its flight before striking the ground. From what height was it released?"
Last two seconds
Total flight
v
v
u ?
u 0
a
10
a
10
s
?
t
?
s
60
2
Q10. Car At is travelling
at 30 𝑚𝑠 −1 . Car B is travelling in the same direction at 20 𝑚𝑠 −1 .
If Car B is 250 metres ahead of Car A, how long before it is overtaken by Car A.
A. 24 s
C. 5 s
Q11. What distance did Car A travel while overtaking car B ?
B29.
A bird flying vertically upwards at 3 𝑚𝑠 −1 drops a fish.
How far apart are bird and fish after 4 seconds ?
B. 25 s
D. 30 s
A. 250 m
B. 500 m
C. 600 m D. 750 m
A. 60 m
B. 70 m
C. 80 m
D. 90 m
Draw and analyse distance–time graphs, displacement–time graphs, velocity–time graphs and acceleration–time
graphs. (Students should be able to sketch and label these graphs for various situations. They should also be able to write
descriptions of the motions represented by such graphs.)
Exercise:
A ball is rolled at 5 𝑚𝑠 −1 along a flat smooth floor. It bounces off a wall, and rebounds at 3 𝑚𝑠 −1 .
(Displacement is measured from point P which is 10 m from the wall.)
(i) Draw a velocity-time graph for t = 0 to t = 6 seconds.
(ii) Draw a speed-time graph for t = 0 to t = 6 seconds.
P
(iii) Draw a displacement-time graph for t = 0 to t = 6 seconds.
(iv) Draw a distance-time graph for t = 0 to t = 6 seconds.
Q*.
A ball is thrown straight up from a cliff, and lands in the sea below. Its speed-time relationship is:
A.
B.
C.
D.
Q16. Which graph below represents the velocity-time relationship for a falling apple?
A.
B.
C.
D.
Q17.
A ball rolls down a smooth ramp. Which graph shows distance travelled each second against time?
A.
B.
C.
D.
Q18.
A ball is dropped on a hard surface and makes several bounces before coming to rest.
Which graph shows velocity versus time?
A.
B.
C.
D.
Q19. A girl jumps up and down several times on a trampoline. Which graph shows her acceleration versus time ?
A.
Q20.
B.
C.
D.
A car accelerates uniformly from rest. It then continues at constant speed before the brakes are applied,
bringing the car to rest. Which graph shows acceleration versus time?
A.
B.
C.
D.
Calculate and interpret the gradients of displacement–time graphs and velocity–time graphs, and the areas
under velocity–time graphs and acceleration–time graphs.
Consider this velocity time graph.
v
Q21.
Q22.
At how many points is the acceleration zero?
How many times does the object change direction?
Q23.
The velocity-time graph below shows the motion of a car
and a truck that are initially beside each other at
time t = 0. The truck is moving at constant speed.
When the two lines intersect the car has travelled….
A.
C.
Q24.
the same distance as the truck
half the distance the truck has
B.
D.
t
twice the distance the truck has
four times the distance the truck has
Joseph runs along a long straight track.
The variation of his speed v with time t is shown.
After 25 seconds Joseph has run 200 m.
Which of the following is correct at 25 seconds?
A.
B.
C.
D.
Q3.
Instantaneous speed / 𝑚𝑠 −1
8
8
10
10
Average speed / 𝑚𝑠 −1
8
10
8
10
What can be determined from a speed-time graph of a particle travelling in a straight line?
A.
B.
C.
D.
Only the magnitude of the acceleration at a given instant
Both the velocity and the acceleration at a given instant
Only the distance travelled in a given time
Both the distance travelled in a given time and the magnitude of the acceleration at a given instant
Q25. Consider a graph showing the variation with time t of the velocity v of an object moving on a straight-line.
Which of the graphs below best represents the variation with time t of the acceleration a of the object?
v
A.
B.
C.
D.
t
Q1.
A glider travels on a friction-free linear air track, bouncing back and forth between elastic buffers.
The shaded area on the glider's velocity time graph represents
A. the length of the track
C. the acceleration of the glider
Q2.
B. half the length of the track
D. the time to travel between the buffers
The graph shows the variation with time t of the acceleration a of an object.
What is the change in velocity of the object in the time interval 0 to 4 s?
A. –8 𝑚𝑠 −1
B. –4 𝑚𝑠 −1
C. +4 𝑚𝑠 −1
D. +8 𝑚𝑠 −1
Describe the effects of air resistance on falling objects.
Only qualitative descriptions are expected.
Students should understand what is meant by terminal speed.
Q26.
The acceleration of a ball dropped from a tall building
(with air resistance taken into account)
A. increases linearly
C. remains constant
B. increases exponentially
D. decreases until it is zero
How would you calculate
the terminal speed?
Q27. Which graph shows speed versus time when a raindrop
falling from rest at time t = 0 reaches terminal velocity?
A.
B.
C.
D.
Q28. A ball, initially at rest, is dropped in the air from a great height. Air resistance is not negligible.
Which of the following graphs best shows the variation with time t of the acceleration a of the ball?
A.
B.
C.
D.
Q29.
A ping-pong ball released at the bottom of a swimming pool accelerates towards the surface.
It reaches terminal velocity after travelling half the distance to the surface.
Which of the following best shows velocity versus distance?
A.
B.
C.
D.
Q30.
Two identical stones are dropped from a tall building, one after the other.
As they fall, what happens to the distance between them if there is air resistance?
A.
C.
It increases
It remains constant
B.
D.
It decreases
It increases up to a constant distance
If an object falls from rest its displacement is proportional to t2
!!
A ball falling under gravity is mathematically the same as a car accelerating uniformly from rest.
So if the car is photographed at equal time intervals, the distances travelled during each interval
are in the ratio 1 : 3 : 5 : 7.
The distance travelled in the fourth second is ___ times the distance travelled in the first second.
The displacement after the fourth second is ___ times the displacement after the first second.
The speed after 4 seconds is ____ times the speed after the first second.
Q13.
Two identical objects A and B fall from rest from different heights.
B takes twice as long as A to reach the ground.
What is the ratio of heights from which they fell?
A. 1 : √2
C. 1 : 4
B. 1 : 2
D. 1 : 8
In the following questions a racing car accelerates uniformly from rest along a straight track.
Q14.
Marker 1 is half way between the start and Marker 2. Where is the car's instantaneous speed 70 𝑘𝑚. ℎ−1 ?
Marker 2
Marker 1
A.
Q15.
B.
C.
Speed = 140 𝑘𝑚. ℎ−1
D.
A. √1.5 : 1
C.
2:1
What is the ratio of the speed of the car at Marker 3
to the speed of the car at Marker 2?
Determine RELATIVE VELOCITY in one and in two dimensions.
Q31.
Marker 3
This question is tricky
because it looks at equal
distances, not equal time
intervals!
B. √3 : 1
D. 3 : 1
vab = va - vb
vab = vac + vcb
Consider two cars A and B. Their velocity vectors are shown.
Car A is travelling twice as fast as Car B. The velocity of A relative to B is
A.
B.
C.
D.
Q32. You are watching a bird fly past from left to right. It releases an object it was holding, that then falls to the ground.
The path of the object as seen by you is
A.
B.
C.
D.
Q33.
Arthur stands on a platform watching a carriage travel past.
(Consider to the right as the positive direction.)
His friend Roger is walking slowly towards the back of the carriage.
Arthur’s velocity with respect to Roger is
A. 22 𝑚𝑠 −1
Q34.
B. 18 𝑚𝑠 −1
ms1
D. −18𝑚𝑠 −1
C. −22 𝑚𝑠 −1
2
ms1

A car is heading east at 10 𝑚𝑠 −1 while a bird is heading north at 4 𝑚𝑠 −1 .
What is the velocity of the bird relative to the car?
A.
Q35.
20
B.
C.
D.
The relative velocity between two objects will be zero only if both are
A.
C.
at rest
travelling at the same speed
B.
D.
travelling at constant speed
travelling at the same speed in the same direction
Q4.
A boat is sailing due north with respect to the water, which is flowing due east.
The velocity of the Earth with respect to the boat is in the direction
Q8.
Consider two identical balls P and Q. At the instant P is dropped off a cliff,
Q is projected horizontally at 10 𝑚𝑠 −1 . After one second the velocity
of P relative to Q will be …
A.
B.
C.
D.
A. SE
C. NE
B. NW
D. SW
Q
P