$A$ 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 $km\, h^{-1}$).

$A$ car is moving on a straight road with uniform acceleration. The following table gives the speed of the car at various instants of time.

Time $(s)$	$0$	$10$	$20$	$30$	$40$	$50$
Speed $(m s^{-1})$	$5$	$10$	$15$	$20$	$25$	$30$

$(i)$ Draw the speed-time graph representing the above set of observations.
$(ii)$ Find the acceleration of the car.

$A$ motor bike running at $90 \, km \, h^{-1}$ is slowed down to $54 \, km \, h^{-1}$ by the application of brakes over a distance of $40 \, m$. If the brakes are applied with the same force,calculate $(i)$ the total time in which the bike comes to rest and $(ii)$ the total distance travelled by the bike.

The velocity$-$time graph of a body has a negative slope. The body is undergoing

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.

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