Question

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

• A. \(t^{\frac{1}{2}}\)
• B. t
• C. \(t^{ \frac{3}{2}}\)
• D. t ²

Answer 1

The Correct Option is B

(ii) t
Mass of the body = m
Acceleration of the body = a
Using Newton’s second law of motion, the force experienced by the body is given by the equation:
F = ma
Both m and a are constants. Hence, force F will also be constant.
F= ma = Constant … (i)
For velocity v, acceleration is given as, a = dv / dt = constant
dv = Constant × dt
v = at ....(ii)
Where, a is another constant
v ∝ t ...(iii)
Power is given by the relation: P = F.v
Using equations (i) and (iii), we have: p ∝ t
Hence, power is directly proportional to time.