Four persons $P, Q, R$ and $S$ are initially at the four corners of a square of side $d$. Each person now moves with a constant speed $v$ in such a way that $P$ always moves directly towards $Q$,$Q$ towards $R$,$R$ towards $S$,and $S$ towards $P$. The four persons will meet after time:

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?

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:

$A$ body is moving with velocity $30 \; m/s$ towards east. After $10 \; s$,its velocity becomes $40 \; m/s$ towards north. The average acceleration of the body is ...... $m/s^2$.

$A$ body of mass $1\, kg$ tied to one end of a string is revolved in a horizontal circle of radius $0.1\, m$ with a speed of $3$ revolutions per second. Assuming the effect of gravity is negligible,the linear velocity,acceleration,and tension in the string will be:

$A$ particle crossing the origin at time $t=0$,moves in the $xy$-plane with a constant acceleration $a$ in the $y$-direction. If the equation of motion of the particle is $y = bx^2$ (where $b$ is a constant),then its velocity component in the $x$-direction is