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Deriving equations of motion from power and mass

  1. Jul 6, 2013 #1
    I'm terrible at calculus and am trying an exercise to hopefully help me understand it better. I want to derive the equations of acceleration, velocity and position of a car with known power and mass. As the car's speed increases, the acceleration will decrease.

    force = mass/acceleration
    power = force*velocity

    So acceleration = power/(velocity*mass)
    velocity = ?
    position = ?

    The integral of acceleration is the velocity but how is the integral done in this case since velocity is an unknown function?
  2. jcsd
  3. Jul 6, 2013 #2


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    Assuming you are talking about a fixed power and mass, we can write "acceleration= power/(velocity*mass)" as [itex]dv/dt= P/(vm)[/itex] and separate- [itex]dv/v= (P/m)dt[/itex]. Integrating both sides, [itex]ln(v)= (P/m)t+ c[/itex] or [itex]v= Ce^{(P/m)t}[/itex] where [itex]C= e^c[/itex] is a constant equal to the initial velocity. Integrating that with respect to t, [itex]x= C(m/P)e^{(P/m)t}+ D[/itex].
  4. Jul 7, 2013 #3
    If initial velocity is zero at time = 0, what is the constant C?

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