The displacement \((x)\) of a point moving in a straight line is given by; \(x=8t^2-4t.\) Then the velocity of the particle is zero at:

1.	\(0.4\) s	2.	\(0.25\) s
3.	\(0.5\) s	4.	\(0.3\) s

The velocity v of an object varies with its position x on a straight line as $\mathrm{v}=3\sqrt{\mathrm{x}}$. Its acceleration versus time (a-t) graph is best represented by:

1.		2.
3.		4.

A particle is moving along the x-axis such that its velocity varies with time as per the equation $\mathrm{v}=20\left(1-\frac{\mathrm{t}}{2}\right)$. At t=0 particle is at the origin. From the following, select the correct position (x) - time (t) plot for the particle:

1.		2.
3.		4.

Suppose you are riding a bike with a speed of 20 m/s due east relative to a person A who is walking on the ground towards the east. If your friend B walking on the ground due west measures your speed as 30 m/s due east, find the relative velocity between two reference frames A and B:-

1. The velocity of A with respect to B is 5 m/s towards the east

2. The velocity of A with respect to B is 5 m/s towards the west

3. The velocity of A with respect to B is 10 m/s towards the east

4. The velocity of A with respect to B is 10 m/s towards the west

An elevator whose floor to ceiling height is 12 meters, moves upward with an acceleration of $2.2$ $\mathrm{m}/{\mathrm{s}}^2$. After 1.5 seconds since starting, a bolt falls from its ceiling. The time taken by the bolt to reach the floor is

1. 1 s

2. 2 s

3. $\sqrt{2}$ s

4. $\sqrt{3}$ s

The position (x) of a particle in a straight line motion is given by $\mathrm{x}=2+10\mathrm{t}-5{\mathrm{t}}^2$ $\left(\mathrm{m}\right)$. Its velocity (v) is best represented by?

1.		2.
3.		4.

A body starting from rest moves with uniform acceleration on a horizontal surface. The body covers 3 consecutive equal distances from the beginning in time ${\mathrm{t}}_1,$ ${\mathrm{t}}_2 , \mathrm{and}$ ${\mathrm{t}}_3$ seconds. The ratio of ${\mathrm{t}}_1:{\mathrm{t}}_2:{\mathrm{t}}_3$ is:
1. 1: 2 : 3
2. $1:\sqrt{2}:\sqrt{3}$
3. $1:(\sqrt{2}-1):(\sqrt{3}-\sqrt{2})$
4. $\sqrt{3}:\sqrt{2}:1$

A ball is thrown vertically downwards with a velocity of \(20\) m/s from the top of a tower. It hits the ground after some time with the velocity of \(80\) m/s . The height of the tower is: (assuming $\mathrm{g}=10$ $\mathrm{m}/{\mathrm{s}}^2)$

A particle starts from rest (with constant acceleration) and acquires velocity 20 m/s in 5s. The distance travelled by the particle in the next 2 s will be:

A drunkard walking in a narrow lane takes \(5\) steps forward and \(3\) steps backward, followed again by \(5\) steps forward and \(3\) steps backward, and so on. Each step is \(1\) m long and requires \(1\) s. There is a pit on the road \(13\) m away from the starting point. The drunkard will fall into the pit after:
1. \(37\) s
2. \(31\) s
3. \(29\) s
4. \(33\) s