$A$ train is travelling at a speed of $90\, km\, h^{-1}$. Brakes 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. (in $, m$)

How much momentum will a dumbbell of mass $10\, kg$ transfer to the floor if it falls from a height of $80\, cm$? Take its downward acceleration to be $10\, m \,s^{-2}$.

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 is $+g$).

$A$ piece of stone is thrown vertically upwards. It reaches its maximum height in $3 \ s$. If the acceleration of the stone is $9.8 \ m s^{-2}$ directed towards the ground,calculate the initial velocity of the stone with which it is thrown upwards. Find the maximum height attained by it.

$A$ motorboat starting from rest on a lake accelerates in a straight line at a constant rate of $3.0 \, m s^{-2}$ for $8.0 \, s$. How far does the boat travel (in $m$) during this time?

Starting from rest at the top of an inclined plane, a body reaches the bottom of the inclined plane in $4$ seconds. In what time does the body cover one-fourth of the distance starting from rest at the top?