A body is moved along a straight line by a machine delivering a constant power. The distance moved by the body in time ' t ' is proportional to

Step-by-step solution

Power = F. V F = m ( dV dt ) m v dV dt = constant = C dV dt = C m = k vdv = kdt vdv = kdt V ^2 2 = kt + c v ( t )^ 1 / 2 ds dt = c t ^ 1 / 2 ds = ( c t ^ 1 / 2 ) dt S = C 2 3 t ^ 3 / 2 S = ct ^ 3 / 2 3 / 2 s t ^ 3 / 2