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.

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.

A particle is moving along the positive x-axis with some initial velocity. The acceleration-time graphs are shown. In which case the velocity of the particle will increase for the entire time between \(t_1\) and \(t_2\)?

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

    
Which of the following statements is true?

Two stones are thrown vertically up simultaneously with different velocities. Which of the following graphs represents the relative separation \((\Delta y)\) between them as a function of time \((t)\)?

1.		2.
3.		4.

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.