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elitewarr
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Homework Statement
The rocket sled has a mass of 4 Mg and travels along the smooth horizontal track such that it maintains a constant power output of 450 kW. Neglect the loss of fuel mass and air resistance, and determine how far the sled must travel to reach a speed of v = 60 m>s starting from rest.
Homework Equations
P = Fv
## E_k = \frac{1}{2} mv^2 ##
W=Fs
The Attempt at a Solution
Since the rocket sled is moving along a flat surface, and that there is no loss of energy, we can conclude that the energy coming from the power output will be converted to kinetic energy.
## E_k = W = Fs = \frac{P}{v} s ##
Thus simplifying, we get
## \frac{1}{2} mv^3 = Ps ##
But apparently, there is something wrong with the equations since if we go about from another way,
## P = Fv = (ma)v = (mv\frac{dv}{ds})v ##
## \int_0^s P \, ds = m\int_0^v v^2 \, dv ##
## Ps = \frac{1}{3} mv^3 ##
Is there something wrong with my concept or that I am not seeing?
Thank you.