An object of mass 'm' initially at rest on a smooth horizontal plane starts moving under the action of force F = 2N. In the process of its linear motion, the angle $$\theta$$ (as shown in figure) between the direction of force and horizontal varies as $$\theta=\mathrm{k}x$$, where k is a constant and $$x$$ is the distance covered by the object from its initial position. The expression of kinetic energy of the object will be $$E = {n \over k}\sin \theta $$. The value of n is ___________.

A body of mass 1kg begins to move under the action of a time dependent force $$\overrightarrow F = \left( {t\widehat i + 3{t^2}\,\widehat j} \right)$$ N, where $$\widehat i$$ and $$\widehat j$$ are the unit vectors along $$x$$ and $$y$$ axis. The power developed by above force, at the time t = 2s, will be ____________ W.

A spherical body of mass 2 kg starting from rest acquires a kinetic energy of 10000 J at the end of $$\mathrm{5^{th}}$$ second. The force acted on the body is ________ N.

A block of mass '$$\mathrm{m}$$' (as shown in figure) moving with kinetic energy E compresses a spring through a distance $$25 \mathrm{~cm}$$ when, its speed is halved. The value of spring constant of used spring will be $$\mathrm{nE} \,\,\mathrm{Nm}^{-1}$$ for $$\mathrm{n}=$$ _________.