"The direction in which an object moves is given by the direction of velocity of the object and not by the direction of acceleration." Give an example to justify this statement.

$(a)$ Draw velocity-time graphs for the following cases:
$(i)$ When the object is at rest.
$(ii)$ When the object is thrown vertically upwards.
$(b)$ $A$ motorcyclist riding motorcycle $A$ who is travelling at $36 \, km \, h^{-1}$ applies the brakes and stops the motorcycle in $10 \, s$. Another motorcyclist of motorcycle $B$ who is travelling at $18 \, km \, h^{-1}$ applies the brakes and stops the motorcycle in $20 \, s$. Plot the speed-time graph for the two motorcycles. Which of the two motorcycles travelled farther before it came to a stop?

Name the physical quantities denoted by:
$(i)$ The slope of the distance$-$time graph.
$(ii)$ The area under a velocity$-$time graph.
$(iii)$ The slope of a velocity$-$time graph.

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?

When is the acceleration $(i)$ positive and $(ii)$ negative?

$(a)$ $A$ 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.