Question

A body is moving along a straight line by a machine delivering constant power. The distance covered by the body in time `t` is proportional to `t^n`, then `n` is ??

Answer 1

`n = 3/2`

Explanation:

Assuming no friction losses and maintaining the same potential energy

`W = (dE)/(dt) = C_0` so

`E = C_0 t = 1/2mv^2` Mechanical Kinetic Energy.

`d = int v dt = int (2C_0)/m sqrt t dt = (2C_0)/m int sqrtt dt = 2/3 (2C_0)/m t^(3/2) = k t^(3/2)`