Work done in time $t $ on a body of mass $m$ which is accelerated from rest to a speed $v$ in time ${t_1}$ as a function of time $t$ is given by
$\frac{1}{2}m\frac{v}{{{t_1}}}{t^2}$
$m\frac{v}{{{t_1}}}{t^2}$
$\frac{1}{2}{\left( {\frac{{m\,v}}{{{t_1}}}} \right)^2}{t^2}$
$\frac{1}{2}m\frac{{{v^2}}}{{t_1^2}}{t^2}$
A shell of mass $m$ moving with velocity $v$ suddenly breakes into two pieces. The part having mass $\frac{m}{5}$ remains stationary. The velocity of the other part will be
A mass $m$ moving horizontally with velocity $v_0$ strikes a pendulum of mass $m$. If the two masses stick together after the collision, then the maximum height reached by the pendulum is
A shell is fired from a canon with a velocity $V$ at an angle $\theta$ with the horizontal direction. At the highest point in its path, it explodes into two pieces of equal masses. One of the pieces come to rest. The speed of the other piece immediately after the explosion is
Four particles $A, B, C$ and $D$ of equal mass are placed at four corners of a square. They move with equal uniform speed $v$ towards the intersection of the diagonals. After collision, $A$ comes to rest, $B$ traces its path back with same speed and $C$ and $D$ move with equal speeds. What is the velocity of $C$ after collision
The force acting on a body moving along $x-$ axis varies with the position of the particle as shown in the figure. The body is in stable equilibrium at