$A$ particle $A$ moves along the line $y=30 \ m$ with a constant velocity $v$ parallel to the $x$-axis. At the moment particle $A$ passes the $y$-axis, a particle $B$ starts from the origin with zero initial speed and a constant acceleration $a=0.40 \ m/s^2$. The angle between $a$ and the $y$-axis is $60^{\circ}$. If the particles $A$ and $B$ collide after some time, then the value of $|v|$ will be (in $m/s$)

$A$ rod $P$ of length $1 \ m$ is hinged at one end $A$ and there is a ring attached to the other end by a light inextensible thread. Another long rod $Q$ is hinged at $B$ and it passes through the ring. The rod $P$ is rotated about an axis which is perpendicular to the plane in which both the rods are present and the variation between the angles $\theta$ and $\phi$ is plotted as shown. The distance between the hinges $A$ and $B$ is ........ $m$.

The diameter of a car wheel is $60 \ cm$. How many radians of angular displacement will the wheel have undergone while the car travels a distance of $1.2 \ km$?

$A$ body of mass '$m$' is projected with a speed '$u$' making an angle of $45^{\circ}$ with the ground. The angular momentum of the body about the point of projection, at the highest point is expressed as $\frac{\sqrt{2} mu^3}{Xg}$. The value of '$X$' is

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

$A$ particle moves once around a circle of radius $1 \,m$. The time taken is $10 \,s$. The average velocity of the motion is