A body is moving indirectionally under the influence of a source of constant power . Its displacement in time t is proportional to

Options

A. `t^(1/2)`
B. t
C. `t^(3/2)`
D. `t^(2)`

Answer

C

Explanation

` :. W = Pt ` [ Work = Power `xx` Time]
` :. 1/2 mv^(2) = Pt [ :. W = K - K_(0) " here "K_(0)=0] `
` :. v =sqrt((2Pt)/m)`
` :. (dx)/(dt) =sqrt((2Pt)/m) " "( :. v =(dt)/dt)`
Power P=Force F `xx` velocity v
` :. " P = ma " xx " at " [ :. " F = ma , v =at "]`
` :. P= ma^(2)t`
` :.a = sqrt(P/(mt))`
Now, from equation (3) of motion of constant acceleration,
In `x = 1/2 sqrt(P/((mt))xxt^(2)`
` :. x = 1/2 sqrt(P/m)xxt^(3/2)`
` :. x prop t^(3/2) " " [ :. " P and m are constant"]`