Work, Energy and Power NCERT Solutions Class 11 Physics - Solved Exercise Question 6.10

Question 6.10:
A body is moving unidirectionally under the influence of a source of constant power. Its displacement in time t is proportional to
(i) t1/2   (ii) t   (iii) t3/2   (iv) t2

Solution:
Power is given by the relation:
P = Fv
= mav = mv(dv/dt) = Constant (say, k)
∴ vdv = (k/m) dt
Integrating both sides:
v2 / 2 = kt / m
v = (2kt / m)1/2
For displacement x of the body, we have
v = dx / dt = (2kt / m)1/2
dx = k' t1/2dt
Where k' = (2k / 3)1/2 = New constant
On integrating both sides, we get:
x = 2k't3/2 / 3
∴ x ∝ t3/2
Option (iii) is the answer

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