A constant power is supplied to an Electric train?

Question by Red Jacket: A constant power is supplied to an Electric train?
The following is a question from the Indian Regional Physics Olympiad.

Assume that a constant power P is supplied to an electric train and is fully used in accelerating the train.Obtain relations giving the velocity of the train and distance traveled by it as functions of time.

Please show detailed working.Thanks.

Best answer:

Answer by Dusty_Looks
Energy supplied is P* t ( at any time t)
E=Pt=Kinetic energy of train
0.5 m v2= Pt
v2= 2P/m * t
v= k * t^0.5 (k- constant)

dx/dt = k * t^ 0.5

Get x as a function of t.
Rearrange above to get t as function of x and substitute in velocity equation.

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