Constant Power

What is the power output of an engine when a car of mass M accelerates with the constant power from rest to a final speed V over a distance d on flat, level ground?

Ignore energy lost due to friction and air resistance.
Derive a formula for the power P in terms of variables: the mass M, the final speed V, and the distance d.
P=P(M,V,d) ?

v=v(t) The speed is a function of time.

Pt = ½m v(t)² Because of the energy conservation law.

v(t)²=2tP/m=(2P/m)t

v(t)=(2P/m)^½t^½

x(t)=(2P/m)^½ (⅔t^3/2)

x(t)²=(2P/m) (⅔)² t³

t=v(t)² / (2P/m)

t³=v(t)⁶ / (2P/m)³

x(t)²=(2P/m) (⅔)² t³=(2P/m) (⅔)² v(t)⁶ / (2P/m)³

x(t)²=(⅔)² v(t)⁶ / (2P/m) ²

x(t)=(⅔) v(t)³ / (2P/m)

2P/m = (⅔) v(t)³ / x(t)

P = ½(⅔) v(t)³m / x(t)

P = ⅓ v(t)³m / x(t) = ⅓ V³m / d