Uniformly accelerated motion and the equations of motion — practice questions

Question 1 · difficulty L2 · understanding

A bus moving along a straight highway with speed of $$72 \mathrm{~km} / \mathrm{h}$$ is brought to halt within $$4 s$$ after applying the brakes. The distance travelled by the bus during this time (Assume the retardation is uniform) is ________ $$m$$.

Question 2 · difficulty L2 · understanding

A car is moving with speed of $$150 \mathrm{~km} / \mathrm{h}$$ and after applying the break it will move $$27 \mathrm{~m}$$ before it stops. If the same car is moving with a speed of one third the reported speed then it will stop after travelling ___________ m distance.

Question 3 · difficulty L2 · understanding

Two cars are travelling towards each other at speed of $$20 \mathrm{~m} \mathrm{~s}^{-1}$$ each. When the cars are $$300 \mathrm{~m}$$ apart, both the drivers apply brakes and the cars retard at the rate of $$2 \mathrm{~m} \mathrm{~s}^{-2}$$. The distance between them when they come to rest is :

• A. 25 m
• B. 100 m
• C. 50 m
• D. 200 m

Question 4 · difficulty L2 · understanding

A body travels $$102.5 \mathrm{~m}$$ in $$\mathrm{n}^{\text {th }}$$ second and $$115.0 \mathrm{~m}$$ in $$(\mathrm{n}+2)^{\text {th }}$$ second. The acceleration is :

• A. $$6.25 \mathrm{~m} / \mathrm{s}^2$$
• B. $$5 \mathrm{~m} / \mathrm{s}^2$$
• C. $$12.5 \mathrm{~m} / \mathrm{s}^2$$
• D. $$9 \mathrm{~m} / \mathrm{s}^2$$

Question 5 · difficulty L2 · understanding

A particle starts with an initial velocity of $$10.0 \mathrm{~ms}^{-1}$$ along $$x$$-direction and accelerates uniformly at the rate of $$2.0 \mathrm{~ms}^{-2}$$. The time taken by the particle to reach the velocity of $$60.0 \mathrm{~ms}^{-1}$$ is __________.

• A. 30s
• B. 6s
• C. 3s
• D. 25s

Question 6 · difficulty L2 · understanding

A small toy starts moving from the position of rest under a constant acceleration. If it travels a distance of 10m in t s, the distance travelled by the toy in the next t s will be :

• A. 10 m
• B. 20 m
• C. 30 m
• D. 40 m

Question 7 · difficulty L2 · understanding

A scooter accelerates from rest for time t 1 at constant rate a 1 and then retards at constant rate a 2 for time t 2 and comes to rest. The correct value of $${{{t_1}} \over {{t_2}}}$$ wil be :

• A. $${{{a_1} + {a_2}} \over {{a_2}}}$$
• B. $${{{a_1} + {a_2}} \over {{a_1}}}$$
• C. $${{{a_2}} \over {{a_1}}}$$
• D. $${{{a_1}} \over {{a_2}}}$$

Question 8 · difficulty L2 · understanding

A gas balloon is going up with a constant velocity of $10 \mathrm{~m} / \mathrm{s}$. When this balloon reached a height of 75 m , a stone is dropped from it and balloon keeps moving up with the same velocity. The height of the balloon when the stone hits the ground is $\_\_\_\_$ m. (Take $g=10 \mathrm{~m} / \mathrm{s}^2$ )

• A. 85
• B. 150
• C. 129
• D. 125

Question 9 · difficulty L2 · understanding

A ball is thrown vertically upward with an initial velocity of $$150 \mathrm{~m} / \mathrm{s}$$. The ratio of velocity after $$3 \mathrm{~s}$$ and $$5 \mathrm{~s}$$ is $$\frac{x+1}{x}$$. The value of $$x$$ is ___________. $$\left\{\right.$$ take, $$\left.g=10 \mathrm{~m} / \mathrm{s}^{2}\right\}$$

• A. $$-5$$
• B. 10
• C. 5
• D. 6

Question 10 · difficulty L2 · understanding

Given below are two statements Statement I : Area under velocity- time graph gives the distance travelled by the body in a given time. Statement II : Area under acceleration- time graph is equal to the change in velocity- in the given time. In the light of given statements, choose the correct answer from the options given below.

• A. Both Statement I and Statement II are False.
• B. Both Statement I and Statement II are true.
• C. Statement I is incorrect but Statement II is true.
• D. Statement I is correct but Statement II is false.