For the motion on a straight line path with constant acceleration,the ratio of the magnitude of the displacement to the distance covered is

Derive the equation $v^{2}-u^{2}=2 a S$ graphically.

Give examples to distinguish:
$(i)$ Distance and displacement.
$(ii)$ Speed and velocity.
$(iii)$ Acceleration and retardation.

Define 'average speed'. An object moves with a uniform speed of $10\, m s^{-1}$ for $5\, s$ and then with a uniform speed of $5\, m s^{-1}$ for $10\, s$. Find its average speed.

What can you conclude about the motion of a body depicted by the velocity-time graphs $(i)$,$(ii)$ and $(iii)$ given below?

The following figure is the speed-time graph for a rocket from the moment when the fuel starts to burn,i.e.,at time $t=0$.
$(a)$ State the acceleration of the rocket at $t=0$.
$(b)$ State what happens to the acceleration of the rocket between $t=5 \, s$ and $t=60 \, s$.
$(c)$ Calculate the acceleration of the rocket at $t=80 \, s$. Give a reason for your answer.
$(d)$ The total mass of the rocket at $t=80 \, s$ is $1.6 \times 10^{6} \, kg$. Calculate the resultant force on the rocket at this time. Give a reason for your answer.