$A$ trolley,while going down an inclined plane,has an acceleration of $2 \,m \,s^{-2}$. What will be its velocity (in $cm \,s^{-1}$) $3 \,s$ after the start?

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 $10\, m \,s^{-2}$.

$A$ stone is thrown in a vertically upward direction with a velocity of $5 \, m s^{-1}$. If the acceleration of the stone during its motion is $10 \, m s^{-2}$ in the downward direction,what will be the height attained by the stone and how much time will it take to reach there?

$A$ 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 (in $m$) the train will go before it is brought to rest.

Draw a velocity-time graph for a body which starts to move with initial velocity $u$ under a constant acceleration $a$ for time $t$. Using this graph,derive an expression for the distance covered $S$ in time $t$.

$A$ scooter starts from rest and moves in a straight line with a constant acceleration,covering a distance of $64 \, m$ in $4 \, s$.
$(i)$ Calculate its acceleration and its final velocity.
$(ii)$ At what time had the scooter covered half the total distance?