A helicopter moving vertically upwards releases a packet when it is at a certain height above the ground. The packet initially moves upwards for a time ${\mathrm{t}}_1$ and then falls downwards for a time ${\mathrm{t}}_2$ until it reaches the ground. Then:

1. ${\mathrm{t}}_1$ < ${\mathrm{t}}_2$

2. ${\mathrm{t}}_1$ = ${\mathrm{t}}_2$

3. ${\mathrm{t}}_1$ > ${\mathrm{t}}_2$

4. Data insufficient

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 $\mathrm{g}=10$ $\mathrm{m}/{\mathrm{s}}^2)$

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

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.

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

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

1.		2.
3.		4.

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:

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

    
Which of the following statements is true?

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 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. $1$ $\mathrm{m}/{\mathrm{s}}^2$