$A$ particle,moving with uniform speed $v$,changes its direction by angle $\theta$ in time $t$. The magnitude of its average acceleration during this time is:

Two particles are projected simultaneously in the same vertical plane,from the same point on the ground,with the same speeds but at different angles $( < 90^o )$ to the horizontal. The path followed by one,as seen by the other,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:

$A$ particle is acted upon by a force of constant magnitude which is always perpendicular to the velocity of the particle. The motion of the particle takes place in a plane. It follows that:

In a circus,a performer throws an apple towards a hoop held at $45 \, m$ height by another performer standing on a high platform (see figure). The thrower aims for the hoop and throws the apple with a speed of $24 \, m/s$. At the exact moment that the thrower releases the apple,the other performer drops the hoop. The hoop falls straight down. At what height above the ground does the apple go through the hoop (in $, m$)?

Two identical discs of same radius $R$ are rotating about their axes in opposite directions with the same constant angular speed $\omega$. The discs are in the same horizontal plane. At time $t=0$,the points $P$ and $Q$ are facing each other as shown in the figure. The relative speed between the two points $P$ and $Q$ as a function of time is best represented by: