A car is moving with velocity v. It stops after applying breaks at a distance of 20 m. If the velocity of the car is doubled, then how much distance it will cover (travel) after applying breaks?
1.  40 m
2.  80 m
3.  160 m
4.  320 m

A body starts falling from height $h$ and if it travels a distance of $\frac{h}{2}$ during the last second of motion, then the time of flight is (in seconds):
1. $\sqrt{2}-1$
2. $2+\sqrt{2}$
3. $\sqrt{2}+\sqrt{3}$
4. $\sqrt{3}+2$

For a particle, displacement time relation is given by; $t$ $=$ $\sqrt{x}$ $+$ $3$ . Its displacement, when its velocity is zero will be:
1. $2$ m
2. $4$ m
3. $0$ m
4. none of the above

A particle starts from rest with constant acceleration. The ratio of space-average velocity to the time-average velocity is:
where time-average velocity and space-average velocity, respectively, are defined as follows: 
$<v>_{time}$ $=$ $\frac{\int v d t}{\int d t}$
$<v>_{space}$ $=$ $\frac{\int v d s}{\int d s}$

The motion of a particle is given by the equation $S = \left(3 t^{3} + 7 t^{2} + 14 t + 8 \right) \text{m} ,$ The value of the acceleration of the particle at $t=1~\text{s}$ is:

A particle is thrown vertically upward. Its velocity at half its height is $10$ m/s. Then the maximum height attained by it is: (Assume, $g=$ $10$ m/s²) 
1. $8$ m
2. $20$ m
3. $10$ m
4. $16$ m

If a ball is thrown vertically upwards with speed $u$, the distance covered during the last $t$ seconds of its ascent is:
1. $ut$
2. $\frac{1}{2}gt^2$
3. $ut-\frac{1}{2}gt^2$
4. $(u+gt)t$

A man throws some balls with the same speed vertically upwards one after the other at an interval of $2$ seconds. What should be the speed of the throw so that more than two balls are in the sky at any time? (Given $g = 9.8$ m/s²)

A ball of mass 2 kg and another of mass 4 kg are dropped together from a 60 feet tall building. After a fall of 30 feet each towards the earth, their respective kinetic energies will be in the ratio of:

1. 1: 4

2. 1: 2

3. 1: $\sqrt{2}$

4. $\sqrt{2}$ :1

The displacement $x$ of a particle varies with time $t$ as $x = ae^{-\alpha t}+ be^{\beta t}$, where $a,$ $b,$ $\alpha,$ and $\beta$ are positive constants. The velocity of the particle will: