$(a)$ A car moving with uniform velocity $'u^{\prime}$ and uniform acceleration $'a^{\prime}$ covers a distance $'S^{\prime}$ in time $'t^{\prime}$. Draw its velocity $-$ time graph and derive an expression relating all the given physical quantities.

$(b)$ A boy revolves a stone tied to a string $0.7 \,m$ long. Find the distance and displacement covered by the stone in completing two revolutions from starting point.

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 rocket at $t=80 s$ Give 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 reason for your answer.

Draw displacement$-$time graphs for the following situations

$(i)$ When body is stationary.

$(ii)$ When body is moving with uniform velocity.

$(iii)$ When body is moving with variable velocity.

A racing car has an acceleration of $4\, m s ^{-2} .$ What distance will it cover in $20$ seconds after start ?

Which of the following is not a vector ?