$A$ particle is moving in a circle with uniform speed. Its motion is

$A$ man is running with constant speed along a circular path of radius $2 \sqrt 2 \, m$. He completes $1$ round in $10 \, s$. Find the instantaneous speed at $2.5 \, s$.

If $\omega_1$ is the angular velocity of the hour hand of a clock and $\omega_2$ is the angular velocity of the Earth,then the ratio $\omega_1 : \omega_2$ is

For a particle in uniform circular motion,the acceleration $\vec{a}$ at any point $P (R, \theta)$ on the circular path of radius $R$ is (when $\theta$ is measured from the positive $x$-axis and $v$ is uniform speed):

The acceleration vector of a particle in uniform circular motion averaged over one complete cycle is a null vector. This statement is:

$A$ particle performing uniform circular motion of radius $\frac{\pi}{2} \,m$ makes $x$ revolutions in time $t$. Its tangential velocity is