$A$ motorcyclist drives from $A$ to $B$ with a uniform speed of $30\, km\, h^{-1}$ and returns back with a speed of $20\, km\, h^{-1}$. Find its average speed (in $km\, h^{-1}$).

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

Draw displacement-time graphs for the following situations:
$(i)$ When a body is stationary.
$(ii)$ When a body is moving with uniform velocity.
$(iii)$ When a body is moving with variable velocity.

$A$ frog hops along a straight line path from point $A$ to point $B$ in $10 \, s$ and then turns and hops to point $C$ in another $5 \, s$. Based on the provided number line,calculate the average speed and average velocity of the frog for the motion between: $(a)$ $A$ to $B$ $(b)$ $A$ to $C$ (through $B$).

State whether the following statement is true or false:
In one-dimensional motion,the average velocity and the instantaneous velocity are unequal.

Derive the following equations for a uniformly accelerated motion:
$(i)$ $v = u + at$
$(ii)$ $S = ut + \frac{1}{2}at^2$
$(iii)$ $v^2 - u^2 = 2aS$, where the symbols have their usual meanings.