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
$\frac{1}{2}m\frac{v}{{{t_1}}}\,{t^2}$
$m\frac{v}{{{t_1}}}\,{t^2}$
$\frac{1}{2}{\left( {\frac{{mv}}{{{t_1}}}} \right)^2}\,{t^2}$
$\frac{1}{2}m\frac{{{v^2}}}{{t_1^2}}\,{t^2}$
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
How much work does a pulling force of $40\, N$ do on the $20\, kg$ box in pulling it $8\, m$ across the smooth floor at a constant speed. The pulling force is directed at $60^o$ above the horizontal .............. $\mathrm{J}$
A simple pendulum of mass $200\, gm$ and length $100\, cm$ is moved aside till the string makes an angle of $60^o$ with the vertical. The kinetic and potential energies of the bob, when the string is inclined at $30^o$ to the vertical, are
A particle moves with a velocity $\vec v\, = \,5\hat i - 3\hat j + 6\hat k\,\,m/s$ under the influence of a constant force $\vec F\, = \,10\hat i + 10\hat j + 20\hat k$. Instantaenous power will be ............... $\mathrm{J} / \mathrm{s}$
The kinetic energy $K$ of a particle moving in a straight line depends upon the distance $s$ as $K = as^2$. The force acting on the particle is