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

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.

The area under the velocity$-$time graph gives the value of

Two stones are thrown vertically upwards simultaneously with their initial velocities $u _{1}$ and $u _{2}$ respectively. Prove that the heights reached by them would be in the ratio of $u_{1}^{2}: u_{2}^{2}$ (Assume upward acceleration is $-\,g$ and downward acceleration to be $+g$.

Write true or false for the following statements

Kinematics deals with the motion of non$-$living objects without taking into account the cause of their motion.

Distance$-$time graph below represents the motion of two buses $A$ and $B$

$(i)$ What is the distance by which bus $B$ was ahead of bus $A$ initially ?

$(ii)$ Do they ever meet each other ? If so, when ?

$(iii)$ What is the distance travelled by bus $A$ when it overtakes bus $B$ ?

$(iv)$ Find out the distance by which bus $A$ was ahead of bus $B$ at $y=12 h$

$(v)$ Which one of them is moving faster ? Give reason.