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

The correct answer is (ii).

Explanation:

From Newton’s first equation of motion,

v = u + at

where, v is the final velocity

u is the initial velocity

a is the acceleration of the body

t is the time taken

Given, u = 0.

So, v = at

Power is given by

P = F × v

⇒ P = ma × at

⇒ P = ma²t

Since m and a are constant,

P ∝ t