The motion of a particle along a straight line is described by the equation; \(x=8+12 t-t^3,\)  where \(x\) is in metre and \(t\) is in second. The retardation of the particle when its velocity becomes zero is:

1.	\(24 ~\text{ms}^{-2} \)	2.	zero
3.	\( 6 ~\text{ms}^{-2} \)	4.	\(12 ~\text{ms}^{-2} \)

A boy standing at the top of a tower of \(20\) m height drops a stone. Assuming \(g=10\) m/s², the velocity with which it hits the ground will be:
1. \(20\) m/s                                         
2. \(40\) m/s
3. \(5\) m/s                                           
4. \(10\) m/s

A particle is projected upwards. The times corresponding to height \(h\) while ascending and while descending are t₁ and t₂ respectively. The velocity of projection will be:
1. \(gt_1\)
2. \(gt_2\)
3. \(g(t_1+t_2)\)
4. \(\frac{g(t_1+t_2)}{2}\)

Four marbles are dropped from the top of a tower one after the other at a one-second interval. The first one reaches the ground after \(4\) seconds. When the first one reaches the ground the distances between the first and second, the second and third, and the third and fourth will be, respectively:

Given below are two statements: 

Acceleration-time graph of a body is shown.

 
The corresponding velocity-time graph of the same body is: 

1.		2.
3.		4.

Which of the following velocity-time graphs shows a realistic situation for a body in motion?

1.		2.
3.		4.

Which graph represents a uniformly accelerated motion?

1.		2.
3.		4.

In the following graph, the distance travelled by the body in metres is: