State whether the following statement is true or false:
$A$ body is said to be at rest if it does not change its position with respect to its reference point.

What is meant by free fall? Two bodies,one of mass $1\,g$ and other of mass $1\,kg$,are dropped from the same height in a vacuum. Compare the two time intervals in which the two bodies will hit the ground.

Two stones are thrown vertically upwards simultaneously with their initial velocities $u_{1}$ and $u_{2}$ respectively. Prove that the heights reached by them would be in the ratio of $u_{1}^{2}: u_{2}^{2}$ (Assume upward acceleration is $-g$ and downward acceleration is $+g$).

If the displacement of a body is proportional to the time elapsed,what type of motion does the body possess?

$A$ train starting from rest picks up a speed of $10\, m s^{-1}$ in $100\, s$. It continues to move at the same speed for the next $250\, s$. It is then brought to rest in the next $50\, s$. Plot a speed-time graph for the entire motion of the train and calculate:
$(i)$ acceleration of the train while accelerating,
$(ii)$ retardation of the train while retarding,
$(iii)$ the total distance covered by the train.

What do you understand by the term acceleration? When is it positive and when is it negative?