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
$\frac{1}{2}\,m\,\frac{v}{{{t_1}}}{\kern 1pt} {t^2}$
$m\,\frac{v}{{{t_1}}}{\kern 1pt} {t^2}$
$\frac{1}{2}\,{\left( {\frac{{mv}}{{{t_1}}}} \right)^2}{\kern 1pt} {t^2}$
$\frac{1}{2}\,m\,\frac{v^2}{{{t^2_1}}}{\kern 1pt} {t^2}$
If the momentum of a body increases by $0.01\%$, its kinetic energy will increase by ........... $\%$
A particle of mass $m$ is moving in a circular path of constant radius $r$ such that its centripetal acceleration $ac$ is varying with time t as $a_c = k^2rt^2$ where $k$ is a constant. The power delivered to the particle by the force acting on it
A body of mass $m$ is accelerated uniformly from rest to a speed $v$ in a time $T$. The instantaneous power delivered to the body as a function of time is given by
A vertical spring with force constant $K$ is fixed on a table. A ball of mass $m$ at a height $h$ above the free upper end of the spring falls vertically on the spring so that the spring is compressed by a distance $d$. The net work done in the process is
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