Kinematics

 

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Kinematics (O Level)

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Question 1
A car accelerates at a rate of $0m{s^{ - 2}}$ for 10 s starting from $3m{s^{ - 1}}$. What is the speed of the car after 10 s?
A
$30m{s^{ - 1}}$
B
$13m{s^{ - 1}}$
C
$3m{s^{ - 1}}$
D
$0m{s^{ - 1}}$
Question 1 Explanation: 
Acceleration is 0, hence there is no change in velocity for the entire period of time.
Question 2
A car accelerates at a rate of $2m{s^{ - 2}}$ for 10 s starting from $3m{s^{ - 1}}$. What is the speed of the car after 10 s?
A
$30m{s^{ - 1}}$
B
$23m{s^{ - 1}}$
C
$20m{s^{ - 1}}$
D
$3m{s^{ - 1}}$
Question 3
A car accelerates from $3m{s^{ - 1}}$ to $15m{s^{ - 1}}$ over a period of 6 seconds. What is its acceleration?
A
$0m{s^{ - 2}}$
B
$2m{s^{ - 2}}$
C
$3m{s^{ - 2}}$
D
$5m{s^{ - 2}}$
Question 4
A car accelerates from $12m{s^{ - 1}}$ to $2m{s^{ - 1}}$ over a period of 5 seconds. What is its acceleration?
A
$2m{s^{ - 2}}$
B
$1m{s^{ - 2}}$
C
$-2m{s^{ - 2}}$
D
$-1m{s^{ - 2}}$
Question 5
A car accelerates from $3m{s^{ - 1}}$ to $15m{s^{ - 1}}$ at a rate of $2m{s^{ - 2}}$. What is the time taken?
A
2 s
B
3 s
C
5 s
D
6 s
Question 6
A car accelerates from rest to $10m{s^{ - 1}}$ in 2 s. What is the distance traveled?
A
2 m
B
5 m
C
10 m
D
20 m
Question 7

A car decelerates from $10m{s^{ - 1}}$ to $5m{s^{ - 1}}$ 2 s. What is the distance traveled?

A
2 m
B
2.5 m
C
5 m
D
10 m
Question 8
A car accelerates from $3m{s^{ - 1}}$ to $15m{s^{ - 1}}$ in 3 s. What is the distance traveled?
A
3 m
B
12 m
C
18 m
D
36 m
Question 9
A car travels at a constant speed of $5m{s^{ - 1}}$ for 2 s, then accelerates $4m{s^{ - 2}}$ for 3 s. What is the distance traveled?
A
28 m
B
43 m
C
46 m
D
61 m
Question 10
A car accelerates from $3m{s^{ - 1}}$ to $9m{s^{ - 1}}$ in 2 s. What is its average speed?
A
$3m{s^{ - 1}}$
B
$6m{s^{ - 1}}$
C
$9m{s^{ - 1}}$
D
$12m{s^{ - 1}}$
Question 11
Which of the following statements about this displacement-time graph is correct?
A
The object travels at constant acceleration
B
The object travels at constant velocity
C
The object travels at constant speed
D
The object is stationary
Question 12
Which of the following statements about this velocity-time graph is the most accurate?
A
The object travels at increasing acceleration
B
The object travels at constant acceleration
C
The object travels at increasing velocity
D
The object travels at constant velocity
Question 12 Explanation: 
Increasing velocity is correct, but has to be at a constant rate of increase. It is as good as saying 'the object is accelerating'. Hence, constant acceleration is the most accurate.
Question 13

Which of the following statements about this displacement-time graph are correct?

A
The object travels at a constant velocity of $3m{s^{ - 1}}$
B
The object travels at a constant acceleration of $3m{s^{ - 2}}$
C
The object travels a distance of 24 m
D
The object is not moving
Question 14

A ball is dropped and takes 3 s to reach the ground. What is the final speed of the ball just before it hits the ground? ($g = 10m{s^{ - 2}}$)

A
$10m{s^{ - 1}}$
B
$20m{s^{ - 1}}$
C
$30m{s^{ - 1}}$
D
$40m{s^{ - 1}}$
Question 14 Explanation: 
$\begin{gathered} v = u + at \hfill \\ v = 0 + 10(3) \hfill \\ v = 30 \hfill \\ \end{gathered} $
Question 15
A ball is thrown downwards at an initial velocity of $10m{s^{ - 1}}$ and takes 3 s to reach the ground. What is the final speed of the ball just before it hits the ground? ($g = 10m{s^{ - 2}}$)
A
$20m{s^{ - 1}}$
B
$30m{s^{ - 1}}$
C
$40m{s^{ - 1}}$
D
$50m{s^{ - 1}}$
Question 16

A ball is thrown downwards at an initial velocity of $10m{s^{ - 1}}$ and takes 3 s to reach the ground. What is the final speed of the ball just before it hits the ground? ($g = 10m{s^{ - 2}}$)

A
$20m{s^{ - 1}}$
B
$30m{s^{ - 1}}$
C
$40m{s^{ - 1}}$
D
$50m{s^{ - 1}}$
Question 16 Explanation: 
$\begin{gathered} v = u + at \hfill \\ v = 10 + 10(3) \hfill \\ v = 40 \hfill \\ \end{gathered} $
Question 17
A ball is thrown vertically downwards at an initial speed of $10m{s^{ - 1}}$ and takes 3 s to reach the ground. What is the final speed of the ball just before it hits the ground? ($g = 10m{s^{ - 2}}$)
A
$10m{s^{ - 1}}$
B
$20m{s^{ - 1}}$
C
$30m{s^{ - 1}}$
D
$40m{s^{ - 1}}$
Question 17 Explanation: 
$\begin{gathered} v = u + at \hfill \\ v = -10 + 10(3) \hfill \\ v = 20 \hfill \\ \end{gathered} $
Question 18
A ball is dropped and takes 3 s to reach the ground. What is displacement of the ball? ($g = 10m{s^{ - 2}}$)
A
20 m
B
25 m
C
30 m
D
45 m
Question 18 Explanation: 
$\begin{gathered} s = ut + \frac{1}{2}a{t^2} \hfill \\ s = 0 + \frac{1}{2}(10){(3)^2} \hfill \\ s = 45 \hfill \\ \end{gathered} $
Question 19
A ball is thrown vertically downwards at an initial speed of \[10m{s^{ - 1}}\] and falls to the ground. This whole process takes 3 s. What is displacement of the ball? ($g = 10m{s^{ - 2}}$)
A
45 m
B
55 m
C
65 m
D
75 m
Question 19 Explanation: 
\[\begin{gathered} s = ut + \frac{1}{2}a{t^2} \hfill \\ s = 10(3) + \frac{1}{2}(10){(3)^2} \hfill \\ s = 75 \hfill \\ \end{gathered} \]
Question 20
A ball is thrown vertically upwards and falls to the ground. This whole process takes 3 s. What is the initial speed of the ball? ($g = 10m{s^{ - 2}}$)
A
\[15m{s^{ - 1}}\]
B
\[20m{s^{ - 1}}\]
C
\[25m{s^{ - 1}}\]
D
\[30m{s^{ - 1}}\]
Question 20 Explanation: 
For the first half of the experiment (ball is thrown and reaches its highest point), time taken is 1.5 s. \[\begin{gathered} v = u + at \hfill \\ 0 = u + 10(1.5) \hfill \\ u = - 15 \hfill \\ \end{gathered} \]
Question 21
A ball is thrown vertically upwards. The time taken for it to reach its highest point is 3 s. What is the displacement of the ball 1 s after the ball is thrown? ($g = 10m{s^{ - 2}}$)
A
20 m
B
25 m
C
30 m
D
35 m
Question 21 Explanation: 
Initial speed of ball: \[\begin{gathered} v = u + at \hfill \\ 0 = u + (-10)(3) \hfill \\ u = 30 \hfill \\ \end{gathered} \] Initial speed of the ball is \[30m{s^{ - 1}}\] Displacement after 1 s. \[\begin{gathered} s = ut + \frac{1}{2}a{t^2} \hfill \\ s = (30)(1) + \frac{1}{2}( - 10)(1) \hfill \\ s = 25 \hfill \\ \end{gathered} \]
Question 22
A ball is thrown vertically upwards at an initial speed of \[23m{s^{ - 1}}\]. How long does it take for the ball to reach the ground again? ($g = 10m{s^{ - 2}}$)
A
2.3 s
B
3.2 s
C
4.6 s
D
6.4 s
Question 22 Explanation: 
Time taken for the ball to reach its maximum height: \[\begin{gathered} v = u + at \hfill \\ 0 = 23 + ( - 10)t \hfill \\ t = 2.3 \hfill \\ \end{gathered} \] Time taken for ball to reach max height then fall back down to the ground: \[2.3 \times 2 = 4.6\]
Question 23
A ball is thrown vertically upwards at an initial speed of \[23m{s^{ - 1}}\]. What is the distance traveled by the ball 3 s after it was thrown? ($g = 10m{s^{ - 2}}$)
A
24 m
B
29 m
C
50 m
D
55 m
Question 23 Explanation: 
Time taken for the ball to reach max height = 2.3 s Distance traveled when max height is reached: \[\begin{gathered} s = ut + \frac{1}{2}a{t^2} \hfill \\ s = (23)(2.3) + \frac{1}{2}( - 10){(2.3)^2} \hfill \\ s = 26.45 \hfill \\ \end{gathered} \] Distance traveled for the remaining 0.7 s. \[\begin{gathered} s = ut + \frac{1}{2}a{t^2} \hfill \\ s = 0 + \frac{1}{2}(10){(0.7)^2} \hfill \\ s = 2.45 \hfill \\ \end{gathered} \] Total distance traveled: \[26.45 + 2.45 = 28.9 \approx 29\]
Question 24

A ball is thrown vertically upwards off a cliff at a speed of \[37m{s^{ - 1}}\] . It falls to the bottom of the cliff after 10 s. What is the height of the cliff? ($g = 10m{s^{ - 2}}$)

A
130 m
B
137 m
C
199 m
D
267 m
Question 24 Explanation: 
Time taken to reach max height: \[\begin{gathered} v = u + at \hfill \\ 0 = 37 + ( - 10)t \hfill \\ t = 3.7 \hfill \\ \end{gathered} \] Distance traveled from the top of the cliff to the max height: \[\begin{gathered} s = ut + \frac{1}{2}a{t^2} \hfill \\ s = (37)(3.7) + \frac{1}{2}( - 10){(3.7)^2} \hfill \\ s = 68.45 \hfill \\ \end{gathered} \] Time taken for ball to travel from max height to bottom of cliff: \[10 - 3.7 = 6.3\] Distance from bottom of cliff to max height \[\begin{gathered} s = ut + \frac{1}{2}a{t^2} \hfill \\ s = (0) + \frac{1}{2}(10){(6.3)^2} \hfill \\ s = 198.45 \hfill \\ \end{gathered} \] Height of the cliff: \[198.45 - 68.45 = 130\]
Question 25

A ball is thrown vertically upwards. It lands on the top of a cliff after attaining a maximum height of 100 m in 7 s. What is the height of the cliff of the ball reaches the top of the cliff after 9 s? What is the height of the cliff? ($g = 10m{s^{ - 2}}$)

A
60 m
B
70 m
C
80 m
D
90 m
Question 25 Explanation: 
Height difference between the max height and the top of the cliff: \[\begin{gathered} s = ut + \frac{1}{2}a{t^2} \hfill \\ s = (0) + \frac{1}{2}(10){(2)^2} \hfill \\ s = 20 \hfill \\ \end{gathered} \] Height of the cliff: \[100 - 20 = 80\]
Question 26
The velocity-time graph of Car A and Car B is shown below. When will the cars meet?
A
5 s
B
7.5 s
C
10 s
D
12.5 s
Question 26 Explanation: 
The area under the velocity-time graph denotes the displacement of the object. Since the area under the velocity-time graphs of both cars is equal when t = 10 s, both cars meet when t = 10 s.
Question 27
The table below shows the velocity of 2 cars at 2 different times. Assuming each car accelerates uniformly. When do the 2 cars meet?
Question 27 Explanation: 
Acceleration of Car A: \[\frac{{14 - 0}}{7} = 2m{s^{ - 2}}\] Acceleration of Car B: \[\frac{{9 - 2}}{7} = 1m{s^{ - 2}}\] Distance traveled by Car A:
Question 28

The table below shows the velocity of 2 cars at 2 different times.

Assuming each car accelerates uniformly. When do the 2 cars meet? 

Question 28 Explanation: 
Acceleration of Car A: \[\frac{{14 - 0}}{7} = 2m{s^{ - 2}}\] Acceleration of Car B: \[\frac{{9 - 2}}{7} = 1m{s^{ - 2}}\] Distance traveled by Car A: \[\begin{gathered} s = ut + \frac{1}{2}a{t^2} \hfill \\ s = 0 + \frac{1}{2}(2){t^2} \hfill \\ s = {t^2} \to (1) \hfill \\ \end{gathered} \] Distance traveled by Car B: \[\begin{gathered} s = ut + \frac{1}{2}a{t^2} \hfill \\ s = 2t + \frac{1}{2}(1){t^2} \hfill \\ s = 2t + \frac{1}{2}{t^2} \to (2) \hfill \\ \end{gathered} \]
Question 29

The table below shows the velocity of 2 cars at 2 different times.

Assuming each car accelerates uniformly. When do the 2 cars meet? 

Question 29 Explanation: 
Acceleration of Car A: \[\frac{{14 - 0}}{7} = 2m{s^{ - 2}}\] Acceleration of Car B: \[\frac{{9 - 2}}{7} = 1m{s^{ - 2}}\] Distance traveled by Car A: \[\begin{gathered} s = ut + \frac{1}{2}a{t^2} \hfill \\ s = 0 + \frac{1}{2}(2){t^2} \hfill \\ s = {t^2} \to (1) \hfill \\ \end{gathered} \] Distance traveled by Car B: \[\begin{gathered} s = ut + \frac{1}{2}a{t^2} \hfill \\ s = 2t + \frac{1}{2}(1){t^2} \hfill \\ s = 2t + \frac{1}{2}{t^2} \to (2) \hfill \\ \end{gathered} \] Since distance traveled by Car A = distance traveled by Car B when both cars meet, (1) = (2), hence, \[{t^2} = 2t + \frac{1}{2}{t^2}\]
Question 30

The table below shows the velocity of 2 cars at 2 different times.

Assuming each car accelerates uniformly. When do the 2 cars meet? 

A
2 s
B
3 s
C
4 s
D
5 s
Question 30 Explanation: 
Acceleration of Car A: \[\frac{{14 - 0}}{7} = 2m{s^{ - 2}}\] Acceleration of Car B: \[\frac{{9 - 2}}{7} = 1m{s^{ - 2}}\] Distance traveled by Car A: \[\begin{gathered} s = ut + \frac{1}{2}a{t^2} \hfill \\ s = 0 + \frac{1}{2}(2){t^2} \hfill \\ s = {t^2} \to (1) \hfill \\ \end{gathered} \] Distance traveled by Car B: \[\begin{gathered} s = ut + \frac{1}{2}a{t^2} \hfill \\ s = 2t + \frac{1}{2}(1){t^2} \hfill \\ s = 2t + \frac{1}{2}{t^2} \to (2) \hfill \\ \end{gathered} \] Since distance traveled by Car A = distance traveled by Car B when both cars meet, (1) = (2), hence, \[\begin{gathered} {t^2} = 2t + \frac{1}{2}{t^2} \hfill \\ \frac{1}{2}{t^2} = 2t \hfill \\ {t^2} = 4t \hfill \\ t = 4{\text{ or }}0 \hfill \\ \end{gathered} \]
Question 31
The displacement-time graph of a truck is shown. When was the truck traveling at \[2m{s^{ - 1}}\]?
A
0 s
B
2 s
C
3 s
D
5 s
Question 31 Explanation: 
The gradient of a displacement-time graph denotes the velocity of the object. The gradient of the graph at t = 5 is 2, hence velocity is \[2m{s^{ - 1}}\]
Question 32
The displacement-time graph of a truck is shown. What is the average velocity of the truck over the 5 s?
A
\[0.4m{s^{ - 1}}\]
B
\[0.6m{s^{ - 1}}\]
C
\[0.8m{s^{ - 1}}\]
D
\[1.0m{s^{ - 1}}\]
Question 32 Explanation: 
Velocity from t = 0 to t = 2: \[0m{s^{ - 1}}\] Velocity from t = 2 to t = 4 \[\frac{{4 - 2}}{{4 - 2}} = 1\] \[1m{s^{ - 1}}\] Velocity from t = 4 to t = 5 \[\frac{{6 - 4}}{{5 - 4}} = 2\] \[2m{s^{ - 1}}\] Average velocity: \[\frac{{(2 \times 0) + (2 \times 1) + (1 \times 1)}}{5} = 0.6\]
Question 33
2 balls are being dropped from different heights. Ball A takes twice the time ball B takes to reach the ground. Which of the following statements are correct?
A
Distance traveled by Ball A is half that of Ball B
B
Distance traveled by Ball A is equal to that of Ball B
C
Distance traveled by Ball A is twice that of Ball B
D
Distance traveled by Ball A is 4 times that of Ball B
Question 33 Explanation: 
Since initial velocity is 0, distance traveled by a ball: \[\begin{gathered} s = ut + \frac{1}{2}a{t^2} \hfill \\ s = 0 + \frac{1}{2}(10){t^2} \hfill \\ s = 5{t^2} \hfill \\ \end{gathered} \] Hence, \[s \propto {t^2}\] If Ball A takes twice the time that Ball B does, its distance traveled will be four times (\[{2^2}\]) that of Ball B.
Question 34
2 balls are dropped from different heights. Ball A is twice the speed of Ball B just before they each reach the ground (at different times). Which of the following statements is correct?
A
Distance traveled by Ball A is half that of Ball B
B
Distance traveled by Ball A is equal to that of Ball B
C
Distance traveled by Ball A is twice that of Ball B
D
Distance traveled by Ball A is four times that of Ball B
Question 34 Explanation: 
The distance traveled by each ball can be expressed as: \[\begin{gathered} {v^2} = {u^2} + 2as \hfill \\ s = \frac{{{v^2} - {u^2}}}{{2a}} \hfill \\ s = \frac{{{v^2} - {{(0)}^2}}}{{2(10)}} \hfill \\ s = \frac{1}{{20}}{v^2} \hfill \\ \end{gathered} \] Hence, \[s \propto {v^2}\] If Ball A's velocity is twice that of Ball B, its displacement will be 4 times that of Ball B.
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