What is the numerical ratio of average velocity to average speed of an object when it is moving along a straight path ?

$(a)$ 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.

Study the speed$-$time graph of a body given below and answer the following questions

$(i)$ What type of motion is represented by $OA, AB$ and $BC$ ?

$(ii)$ Find positive and negative accelerations of the body.

$(iii)$ Find the distance travelled by the body from $A$ to $B$.

A particle accelerates from rest at a constant rate for sometime and attains a constant velocity of $8\, m s ^{-1}$. Afterwards it decelerates with a constant rate and comes to rest. If the total time taken is $4$ second, the distance travelled is

Define velocity.

Give an example of an accelerated body, moving with a uniform speed.