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

$A$ body is thrown vertically upward with velocity $u$,the greatest height $h$ to which it will rise is,

Prove that if a body is thrown vertically upwards,then the time of ascent is equal to the time of descent.

$A$ 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?

$A$ 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?

$A$ 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.