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 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 $g = 10\, ms^{-2}$) :-

A point moves with uniform acceleration and $\upsilon _1,\upsilon _2$ and $\upsilon _3$ denote the average velocities in the three successive intervals of time $t_1, t_2$ and $t_3$. Which of the following relations is correct

The motion of a particle along a straight line is described by equation $x = 8 + 12t -t^3$ where $x$ is in metre and $t$ in second. The retardation of the particle when its velocity becomes zero is.......$ms^{-2}$

A frictionless wire $AB$ is fixed on a circle of radius $R$. A very small bead slips on  this wire. Time taken by bead to slip from $A$ to $B$ is

Figure shows the graph of $x$-coordinate of a particle moving along $x$-axis as a function of time. Average velocity during $t=0$ to $6 \,s$ and instantaneous velocity at $t=3 \,s$ respectively, will be