$A$ girl of mass $50\, kg$ jumps out of a moving boat of mass $300\, kg$ on to the bank with a horizontal velocity of $3\, m s^{-1}$. With what velocity does the boat begin to move backwards (in $, m s^{-1}$)?

$(a)$ Differentiate between uniform linear motion and uniform circular motion.
$(b)$ Write any four examples of uniform circular motion.
$(c)$ Is uniform circular motion an accelerated motion?

$(a)$ $A$ car moving with uniform velocity $u$ and uniform acceleration $a$ covers a distance $S$ in time $t$. 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 the starting point.

In a long distance race,the athletes were expected to take four rounds of the track such that the finish line was the same as the start line. Suppose the length of the track was $200 \ m$.
$(a)$ What is the total distance to be covered by the athletes?
$(b)$ What is the displacement of the athletes when they touch the finish line?
$(c)$ Is the motion of the athletes uniform or nonuniform?
$(d)$ Is the displacement of an athlete and the distance moved by him at the end of the race equal?

Explain the differences between the two graphs.

The distance$-$time graph of a body is parallel to the time axis. The body is