A particle performs circular motion of radius $1 \mathrm{m}$ from rest. The tangential acceleration of the particle at any time $t \left(\mathrm{in} \mathrm{s}\right)$ is given by $a_{\mathrm{t}}=t \left(\mathrm{in} \mathrm{m} {\mathrm{s}}^{-2}\right)$. The radial acceleration of the particle at $t=2 \mathrm{s}$ is

The square of the angular velocity $\omega \left(\mathrm{in} \mathrm{rad} {\mathrm{s}}^{-1}\right)$ of a certain wheel increases linearly with the angular displacement during $100$revolutions of the wheel's motion as shown. Compute the time $t \left(\mathrm{in} \mathrm{rad}\right)$ for given $100$ revolutions.

The figure shows the total acceleration and velocity of a particle moving clockwise in a circle of radius $2.5 \mathrm{m}$ at a given instant of time. At this instant, find $\left(\mathrm{i}\right)$ its radial acceleration,$\left(\mathrm{ii}\right)$ the speed of the particle and $\left(\mathrm{iii}\right)$ its tangential acceleration.