A body is moving undirectionally under the influence of a source of constatn power. It displacement in time t is proportional to (i) `t^(1//2)` (ii) t (iii) `t^(3//2)` (iv) `t^(2)`

Explanation

(iii) `t^(3//2)`
As it is given that the body is moving under the influence of constant power . Power is the rate of doing work . Let the constant power dellievered by the source be P and the work done by the source from t = 0 to t = t is given by W = Pt .
According to work - energy theorem the total work done by a force is equalto change in kinetic energy . Let the velocity attained by the body after t time be v .
Thus , `W = Pt = 1/2 mv^(2)` [ Assuming that the mass of the body is m ]
Thus the velocity of the body is given by :
` v = sqrt((2Pt)/m)` Now , the velocity can be expressed as :
`(dx)/(dt ) = sqrt((2Pt)/m) dt `
`int_(0)^(x) dx = int_(0)^(t) sqrt((2Pt)/m) dt `
`rArr x = sqrt((2p)/m) int_(0)^(t) sqrt(t) dt = sqrt((2P)/m) [ (2t^(3//2))/3] _(0)^(t) = 2/3 sqrt((2p)/m ) t^(3//2)`
Thus , `x prop t^(3//2)`