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. $\sqrt{3}:\sqrt{2}:1$

For the given acceleration \(\left ( a \right )\) versus time \(\left ( t \right )\) graph of a body, the body is initially at rest.

       
From the following, the velocity \(\left ( v \right )\) versus time \(\left ( t \right )\) graph will be:

1.		2.
3.		4.

A particle moves with a velocity $\mathrm{v}={\mathrm{\alpha t}}^3$ along a straight line. The average speed in time interval \(t=0\) to \(t=T\) will be:

1. ${\mathrm{\alpha T}}^3$

2. $\frac{{\mathrm{\alpha T}}^3}{2}$

3. $\frac{{\mathrm{\alpha T}}^3}{3}$

4. $\frac{{\mathrm{\alpha T}}^3}{4}$

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 boy falls from a building of height 320 m. After 5 seconds, superman jumps downward with initial speed u such that the boy can be saved. The minimum value of u is (assume g=10 $\mathrm{m}/{\mathrm{s}}^2$)

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 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:

A body is moving along a straight line according to the equation of motion, x$={\mathrm{t}}^2-3\mathrm{t}+4$, where x is in metre and t is in seconds. What is the acceleration of the body when it comes to rest?

1. Zero

2. $2$ $\mathrm{m}/{\mathrm{s}}^2$

3. $\frac{3}{2}$ $m/s^2$

4. $1$ $\mathrm{m}/{\mathrm{s}}^2$

A particle is allowed to fall from rest from a height \(h\). Which of the following represents its velocity versus time graph?

1.		2.
3.		4.

The graph below shows position as a function of time for two trains running on parallel tracks.

    
Which of the following statements is true?