here is derivation ------------------- power is constant hence--------- F*v = k m*a*v = k m*dv/dt*v = k m*v*dv = kdt intagrating we get ------------ mv^2 = 2kt or v = (2kt/m)^1/2 ds/dt = (2kt/m)^1/2dt again intagrating s =2/3(2kt/m)^1/2 * t^3/2 or s propor. to t3/2