Answer the following questions
$(i)$ State the type of motion shown by a freely falling stone.
$(ii)$ When a stone is thrown vertically upwards its velocity is continuously decreased. Why ?
$(iii)$ Give an example of a motion in which average velocity is zero, but the average speed is not zero.
$(i)$ Uniform motion.
$(ii)$ The stone is continuously being attracted by the earth, this causes retardation in the stone's motion, hence its velocity goes on decreasing continuously
$(iii)$ Uniform circular motion.
Explain with reason, which of the following graphs can possibly represent the motion of a particle observed in nature ?
Draw velocity-time graphs for the following situations
$(i)$ When body is moving with uniform velocity.
$(ii)$ When body is moving with variable velocity, but uniform acceleration.
$(iii)$ When body is moving with variable velocity, but uniform retardation.
$(iv)$ When body is moving with a variable velocity and variable acceleration.
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 $+g$.
A car starts from rest and moves along the $x-$ axis with constant acceleration $5\, ms^{-2}$ for $8\,\sec $. If it then continues with constant velocity, what distance will the car cover in $12\,\sec $ since it started from the rest ?
A train is travelling at a speed of $90\, km h ^{-1}$. Breaks are applied so as to produce a uniform acceleration of $0.5\, m s ^{-2}$. Find how far the train will go before it is brought to rest.