A body is moved in straight line by machine with constant power. The distance travelled by it in time duration t is proportional to

Step-by-step solution

Here, P= constant, or, W t =P W=P t or, W=P t or 1 2 m v^2=P t [Using work-energy theorem] or v^2= 2 P m t or v= 2 P m t^ 1 / 2 or d x= 2 P m t^ 1 / 2 d t Integrating both sides, ₀^x d x= 2 P m ₀^t t^ 1 / 2 d t aligned & x= 2 P m ( 2 3 ) t^ 3 / 2 & x t^ 3 / 2 & or displacement ( time )^ 3 / 2 aligned