A very large number of balls are thrown vertically upwards in quick succession in such a  way that the next ball is thrown when the previous one is at the maximum height. If the  maximum height is $5\, m$, the number of balls thrown per minute is (take $g = 10\, ms^{-2}$) :-

Which of the following option is correct for a object having a straight line motion represented by the following graph ?

A bus is moving with a velocity $10 \,m/s$ on a straight road. A scooterist wishes to overtake the bus in $100\, s$. If the bus is at a distance of $1 \,km$ from the scooterist, with what velocity should the scooterist chase the bus......... $m/s$

A wheel of radius $1$ meter rolls forward half a revolution on a horizontal ground. The magnitude of the displacement of the point of the wheel initially in contact with the ground is

A person travels along a straight road for half the distance with velocity ${v_1}$ and the remaining half distance with velocity ${v_2}$ The average velocity is given by

A particle is projected vertically upwards from a point $A$ on the ground. It takes $t_1$ time to reach a point $B$ but it still continues to move up. If it takes $t_2$ time to reach  the ground from point $B$ then height of point $B$ from the ground is