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

A body is moving along a straight line according to the equation of motion, \(x= t^{2} - 3 t + 4\), 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. \(2~\text{m/s}^2\)
3. \(\frac{3}{2}~\text{m/s}^2\)
4. \(1~\text{m/s}^2\)

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 \(v=3\sqrt{x}.\) Its acceleration versus time \((a\text-t)\) graph is best represented by:

1.		2.
3.		4.

Starting from rest, a car accelerates uniformly at the rate of \(1~\text{m/s}^2\) for some time, then decelerates uniformly at the rate of \(2~\text{m/s}^2\) 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

A particle is moving along the \(x\)-axis such that its velocity varies with time as per the equation \(v = 20\left(1-\frac{t}{2}\right)\). 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 \(B\):