An object moving along horizontal $$x$$-direction with kinetic energy $$10 \mathrm{~J}$$ is displaced through $$x=(3 \hat{i}) \mathrm{m}$$ by the force $$\vec{F}=(-2 \hat{i}+3 \hat{j}) \mathrm{N}$$. The kinetic energy of the object at the end of the displacement $$x$$ is

An object falls from a height of $$10 \mathrm{~m}$$ above the ground. After striking the ground it loses $$50 \%$$ of its kinetic energy. The height upto which the object can rebounce from the ground is:

At any instant of time $$t$$, the displacement of any particle is given by $$2 t-1$$ ($$\mathrm{SI}$$ unit) under the influence of force of $$5 \mathrm{~N}$$. The value of instantaneous power is (in $$\mathrm{SI}$$ unit):

A particle moves with a velocity $$(5 \hat{i}-3 \hat{j}+6 \hat{k}) ~\mathrm{ms}^{-1}$$ horizontally under the action of constant force $$(10 \hat{\mathrm{i}}+10 \hat{\mathrm{j}}+20 \hat{\mathrm{k}}) \mathrm{N}$$. The instantaneous power supplied to the particle is :