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 :

The potential energy of a long spring when stretched by $$2 \mathrm{~cm}$$ is U. If the spring is stretched by $$8 \mathrm{~cm}$$, potential energy stored in it will be :

The restoring force of a spring with a block attached to the free end of the spring is represented by

An electric lift with a maximum load of 2000 kg (lift + passengers) is moving up with a constant speed of 1.5 ms^{$$-$$1}. The frictional force opposing the motion is 3000 N. The minimum power delivered by the motor to the lift in watts is : (g = 10 ms^{$$-$$2})