The position vector of a particle is given as $\vec{r} = (t^2 - 4t + 6)\hat{i} + (t^2)\hat{j}$. The time after which the velocity vector and acceleration vector become perpendicular to each other is equal to ....... $sec$.

The given diagram shows a straight length of tape being wound on to a reel. The reel is rotating about a fixed axis with constant angular velocity and its radius is increasing at a steady rate. Which graph correctly shows the variation with time of the speed $v$ at which the tape moves towards the roll?

$A$ wheel completes $2000$ rotations in covering a distance of $9.5\,km$. The diameter of the wheel is:

$A$ particle crossing the origin at time $t=0$,moves in the $xy$-plane with a constant acceleration $a$ in the $y$-direction. If the equation of motion of the particle is $y = bx^2$ (where $b$ is a constant),then its velocity component in the $x$-direction is

If a particle of mass $m$ covers half of the horizontal circle with constant speed $v$,then the change in its kinetic energy is

An object is moving in a circle of radius $100 \, m$ with a constant speed of $31.4 \, m/s$. What is its average speed for one complete revolution?