Power applied to a particle varies with time as $P = [3t^2 -2t + 1]$ $watt$ then the change in kinetic energy of particle from $t = 2\,sec$ to $t = 4\,sec.$ ............... $\mathrm{J}$

$A$ ball is dropped from height $5m$. The time after which ball stops rebounding if coefficient of restitution between ball and ground $e = 1/2$, is .................. $\mathrm{sec}$

Curve between net forcevs time is shown Initially particle is at rest .. Which of the following best represents the resulting velocity-time graph of the particle ?

The variation of force $F$ acting on a body moving along $x$-axis varies with its position $(x)$ as shown in figure The body is in stable equilibrium state at

Figure shows the vertical section of frictionless surface. A block of mass $2\, kg$ is released from the position $A$ ; its $KE$ as it reaches the position $C$ is ............ $\mathrm{J}$

A body of mass ${M_1}$ collides elastically with another mass ${M_2}$ at rest. There is maximum transfer of energy when