Work, Energy and Power NCERT Solutions Class 11 Physics - Solved Exercise Question 6.9

Question 6.9:
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) t1/2   (ii) t   (iii) t3/2   (iv) t2

Solution:
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 a constant.
F = ma = Constant … (i)
For velocity v, acceleration is given as,
a = dv / dt = Constant
dv = Constant X dt
v = αt   ...(ii)
Where α 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.
Option (ii) is the answer

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