A body is initially at rest. It undergoes one-dimensional motion with constant acceleration. The power delivered to it at time t is proportional to

(i) t^1/2 (ii) t (iii) t^3/2 (iv) t²

State if each of the following statements is true or false. Give reasons for your answer.

A. In an elastic collision of two bodies, the momentum and energy of each body is conserved.

B. Total energy of a system is always conserved, no matter what internal and external forces on the body are present.

C. Work done in the motion of a body over a closed loop is zero for every force in nature.

D. In an inelastic collision, the final kinetic energy is always less than the initial kinetic energy of the system.

Answer carefully, with reasons:

A. In an elastic collision of two billiard balls, is the total kinetic energy conserved during the short time of collision of the balls (i.e. when they are in contact)?

B. Is the total linear momentum conserved during the short time of an elastic collision of two balls?

C. What are the answers to (a) and (b) for an inelastic collision?

D. the potential energy of two billiard balls depends only on the separation distance between their centres, is the collision elastic or inelastic? (Note, we are talking here of potential energy corresponding to the force during collision, not gravitational potential energy).

A body is moving unidirectionally under the influence of a source of constant power. Its displacement in time t is proportional to

(i) t^1/2 (ii) t (iii) t^3/2 (iv) t²

A body constrained to move along the z-axis of a coordinate system is subject to a constant force F given by