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 that power P is constant
As `P = W/t = (F int dx)/t `
= ` ( m int a dx)/t `
` = m/t int v/t dx = m/(t^(2)) int x/t dx `
or `P = m/(t^(3)) int x dx `
or `P = (mx^(2))/(2t^(3))`
or `x^(2) = (2Pt^(3))/m `
As m and P are constant
So `x^(2) prop t^(3)`
or `x prop t^(3//2)`