Two particles $A$ and $B$ start at the origin $O$ and travel in opposite directions along a circular path of radius $0.5\,m$ at constant speeds $0.5\,m/s$ and $1.5\,m/s$,respectively. The time when they collide with each other is ........ $\text{s}$.

$A$ particle moves around a circular path of radius $r$ with uniform speed $V$. After moving half the circle,the average acceleration of the particle is

Will the linear velocity of a particle rotating with a constant angular speed about a non-fixed axis be constant? Why?

$A$ person walks in such a way that he covers equal distance in each step. The person takes $2$ steps forward towards East, then takes a right turn and walks $4$ steps towards South, then takes a right turn and walks $6$ steps towards West, and then takes a right turn and walks further. The direction of his final position after a total of $20$ steps walk with respect to his initial position is:

The kinetic energy $K$ of a particle moving along a circle of radius $R$ depends upon the distance $s$ as $K = as^2$. The force acting on the particle is

From the ground level,a ball is to be shot with a certain speed. The graph shows the range $(R)$ of the particle versus the angle of projection from the horizontal $(\theta)$. The values of $\theta_1$ and $\theta_2$ are: