A circular cycle track has a circumference of $314\, m$ with $A B$ as one of its diameter. $A$ cyclist travels from $A$ to $B$ along the circular path with a velocity of constant magnitude $15.7\, m s ^{-1}$. Find the

$(a)$ distance moved by the cyclist.

$(b)$ displacement of the cyclist, if $A B$ represents north$-$south direction.

$(c)$ the average velocity of the cyclist.

The distance$-$time graph of two trains are given below. The trains start simultaneously in the same direction.

$(i)$ How much ahead of $A$ is $B$ when the motion starts ?

$(ii)$ What is the speed of $B$ ?

$(iii)$ When and where $A$ will catch $B$ ?

$(iv)$ What is the difference between the speeds of $A$ and $B$ ?

$(v)$ Is the speed of either trains uniform or non uniform ? Justify your answer.

An electric train is moving with a velocity of $120\, km h^{-1} .$ How much distance will it corer in $30 \,s$ ?

A cyclist driving at $5\, m s ^{-1}$ picks a velocity of $10\, m s ^{-1}$ over a distance of $50\, m$. Calculate $(i)$ acceleration $(ii)$ time in which the cyclist picks up the above velocity.

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.