A body is moving unidirectionally under the influence of a source of constant power supplying energy. Which of the diagrams shown in figure. Correctly shows the displacement-time curve for its motion ?

Options

A.
B.
C.
D.

Answer

D

Explanation

Power=`(K.E)/(t)=(1/2mv^2)/(t)`
v=`sqrt(t)`
`(ds)/(dt)=t^(1//2)`
ds=`t^(1//2)dt`
s=`(2t^(1//2))/(3)implies s prop t^(1//2)`
Slope of x-t graph is +ve.