An athlete completes one round of a circular track of radius $R$ in $40 \,s$. What will be his displacement at the end of $2 \,min \,20 \,s$?

What is uniform circular motion? By using a proper figure,derive the equation for centripetal acceleration $a_c = \frac{v^2}{r}$ for uniform circular motion. Show that its direction is towards the center.

$A$ particle is performing $U.C.M.$ along the circumference of a circle of diameter $50 \ cm$ with a frequency of $2 \ Hz$. The acceleration of the particle in $m/s^2$ is:

$A$ ball is moving uniformly in a circular path of radius $1 \, m$ with a time period of $1.5 \, s$. If the ball is suddenly stopped at $t = 8.3 \, s$,the magnitude of the displacement of the ball with respect to its position at $t = 0 \, s$ is closest to .......... $m$.

An object moves at a constant speed along a circular path in the horizontal $XY$ plane with the center at the origin. When the object is at $x = -2 \, m$,its velocity is $-(4 \, m/s) \hat{j}$. What is the object's acceleration when it is at $y = 2 \, m$?

$A$ particle is moving on a circular path of radius $r$ with uniform speed $v$. What is the displacement of the particle after it has described an angle of $60^{\circ}$?