The Equations of Motion

Q.

A ball is thrown vertically upwards with a velocity of $49m{s}^{-1}$. Calculate the maximum height to which it rises.

Q.

A body is projected vertically up with velocity u. Its velocity at half its maximum height is?

1. $\sqrt{2u}$

2. $\frac{u}{\sqrt{2}}$

3. $\frac{u}{2d}$

4. $\frac{u^2}{2}$

Q. A plane has a take-off speed of $120m{s}^{-1}$ after covering a distance of $2400m$. Determine the acceleration $\left(a\right)$ of the plane (assuming it to be constant) and the time $\left(t\right)$ required to reach that speed.

1. $a=4m{s}^{-2},t=30s$
2. $a=3m{s}^{-2},t=30s$
3. $a=4m{s}^{-2},t=40s$
4. $a=3m{s}^{-2},t=40s$

Q.

A boy is running along a circular track of radius $7m$. He completes one circle in $10seconds$. The average velocity of the boy is

1. $4.4m{s}^{-1}$

2. $0.7m{s}^{-1}$

3. Zero

4. $70m{s}^{-1}$

Q.

A baseball is popped straight up into the air and has a hang-time of 6 s. Determine the maximum height to which the ball rises?

1. 180 m

2. 90 m

3. 45 m

4. 22.5 m

Q.

A body has an initial velocity of $4m{s}^{-1}$ and deceleration of $4m{s}^{-2}$, then what is its final velocity after travelling 2 m?

1. $5m{s}^{-1}$

2. $2m{s}^{-1}$

3. $4m{s}^{-1}$

4. $0m{s}^{-1}$

Q.

A person standing on the edge of a cliff of height 40 m above the ground throws the first ball straight up with an initial velocity of 20 $\frac{m}{s}$, and then throws the second ball straight down with the same initial velocity 20 $\frac{m}{s}$. What are their respective velocities just before they hit the ground. (Take a = 10 $m/s^2$)

1. 20√2 m/s, 20√2 m/s

2. 20√2 m/s, 20√3 m/s

3. 20√3 m/s, 20√2 m/s

4. 20√3 m/s, 20√3 m/s

Q. A child drops a toy from the top of a building, it takes 1 s to reach the ground. Find the height of the building and the average speed of the toy respectively.
(Take g = $10m{s}^{-2}$)

1. $5mand5m{s}^{-1}$
2. $6mand6m{s}^{-1}$
3. $7mand7m{s}^{-1}$
4. $4mand5m{s}^{-1}$

Q. A lorry and a car with the same kinetic energy are brought to rest by the application of brakes which provide equal retarding forces. Which of them will come to rest in a shorter distance?

1. Lorry
2. Car
3. Both will stop at the same distance
4. Cannot be said

Q.

Brakes are applied to a truck to produce an acceleration of $–10m/s^2$​. If the truck takes $5s$ to stop after applying the brakes, the distance covered by the truck before coming to rest is $250m$.

1. 200 m

2. 125 m

Q. A man running with a uniform speed ‘u’ on a straight road observes a stationary bus at a distance ‘d’ ahead of him. At that instant, the bus starts with an acceleration ‘a’. The condition that he would be able to catch the bus is

1. $d\le \frac{u^2}{a}$
2. $d\le \frac{u^2}{2a}$
3. $d\le \frac{u^2}{3a}$
4. $d\le \frac{u^2}{4a}$

Q.

A ball thrown up vertically returns to the thrower after 12 seconds. Find the maximum height it reaches.

Q.

Match the statements of Column A with those of Column B.

Column A	Column B
(A) Uniform velocity Derived quantity	(a) $Totaldis\tan ce÷Time$
(B) Average speed	(b) $m{s}^{-2}$
(C) Average velocity	(c) Acceleration is zero
(D) Acceleration	(d) Ratio of total displacement to total time taken

1. $A\to c;B\to a;C\to d;D\to b$

2. $A\to a;B\to c;C\to b;D\to d$

3. $A\to c;B\to a;C\to b;D\to d$

4. $A\to a;B\to b;C\to c;D\to d$

Q. A body in uniformly accelerated motion travels 200 cm in the first two seconds and 220 cm in the next four seconds. The velocity at the end of seventh second from start is

1. $5cm{s}^{-1}$
2. $10cm{s}^{-1}$
3. $15cm{s}^{-1}$
4. $20cm{s}^{-1}$

Q.

Average velocity of a particle moving in a straight line, with constant acceleration ‘a’ and initial velocity u in first t seconds is :

1. u

2. u + (at/2)

3. (u + at)/2

4. u + at

Q.

A ball takes t second to fall from a height h₁ and 4t seconds to fall from h₂. then$\frac{h_1}{h_2}$ is

1. 2

2. 4

3. 0.5

4. 0.0625