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?

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.

Starting from rest, a car accelerates uniformly at the rate of $1$ $\mathrm{m}/{\mathrm{s}}^2$ for some time, then decelerates uniformly at the rate of $2$ $\mathrm{m}/{\mathrm{s}}^2$, and finally comes to rest after a journey of 1 minute. The maximum possible speed of the car during this journey is:

1. 10 m/s

2. 20 m/s

3. 30 m/s

4. 40 m/s