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

$A$ particle is moving in the $xy$-plane in a circular path with its center at the origin. If at an instant the position of the particle is given by $\frac{1}{\sqrt{2}}(\hat{i}+\hat{j})$,then the velocity of the particle is along .......

Two balls are thrown as shown in the figure and they reach the ground in the same time. What is the ratio of the maximum heights attained by them?

$A$ particle moves towards east with velocity $5\, m/s$. After $10\, s$,its direction changes towards north with the same velocity. The average acceleration of the particle is

$A$ particle of mass $m$ performs uniform circular motion of radius $r$ with linear speed $v$ under the application of force $F$. If $m$,$v$,and $r$ are all increased by $20 \%$,the necessary change in force required to maintain the particle in uniform circular motion is: (in $\%$)

$A$ particle of mass $m$ moves along a circular path of radius $r$ with a time-dependent centripetal acceleration $a_c = k^2rt^2$,where $k$ is a constant. What is the power delivered to the particle by the force acting on it?