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

B

Explanation

Given, power = constant
We know that power (P)
`P=(dW)/(dt) = (F.ds)/(dt) = (F ds)/(dt)`
( `:. ` body is moving unidirectionally)
Hence, F.ds = Fds `cos 0^@`
`P=(Fds)/(dt) `= constant ( `:.` P = constant by question)
Now, writing dimensions
Now, writing dimensions
[F][v] = constant
`implies [MLT^(-2)][LT^(-1)]=` constant ( `:.` Mass is constant)
`implies L prop T^(3//2) implies` Displacement (d ) `prop t^(3//2)`