$A$ car runs at a constant speed on a circular track of radius $100\,m$,taking $62.8\,s$ for every circular lap. The average velocity and average speed for each circular lap respectively are:

If at any point on the path of a projectile its velocity is $u$ at an inclination $\alpha$ to the horizontal,then after what time will it move at right angles to its former direction?

$A$ ball of mass $100 \ g$ is projected with velocity $20 \ m/s$ at $60^{\circ}$ with the horizontal. The decrease in kinetic energy of the ball during the motion from the point of projection to the highest point is:

Three point particles $P, Q, R$ move in a circle of radius $r$ with different but constant speeds. They start moving at $t = 0$ from their initial positions as shown in the figure. The angular velocities (in $\text{rad/s}$) of $P, Q$ and $R$ are $5\pi, 2\pi$ and $3\pi$ respectively,in the same sense. The number of times $P$ and $Q$ meet in the time interval $t = 0$ to $t = 1 \text{ s}$ is:

$A$ particle moves in the $XY$-plane with $x$ and $y$ coordinates varying with time $t$ as $x(t) = 5t$ and $y(t) = 5t(27 - t^2)$. At what time $t$ (in seconds) will the direction of velocity and acceleration be perpendicular to each other?

$A$ projectile is thrown with velocity $v$ making an angle $\theta$ with the vertical. It reaches a maximum height $H$. The time of flight is: