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Linear motion with variable forces

  1. Jun 26, 2012 #1
    1. The problem statement, all variables and given/known data
    A racing car of mass 20000kg accelerates with a driving force of 480(t-10)^2 newtons until it reaches its maximum speed after 10 seconds. Find its maximum speed, and the distance it travels in reaching this speed.





    3. The attempt at a solution
    Again, I can't seem to get the distance travelled after the second integration.
    m=2000kg
    F=480(t-10)^2
    a=F/m
    = 6(t-10)^2/25
    v=∫a dt
    =[6(t-10)^3/3]/25 + k
    Since t=0, v=0 and therefore v=[6(t-10)^3/3]/25
    Vmax is found out to be 80m/s

    But integration of v did not give me the answer stated, which is 600m. I got 200m instead.

    Please include detailed explanations along with the solution. Thanks! :D
     
  2. jcsd
  3. Jun 26, 2012 #2
    What is the mass?
     
  4. Jun 27, 2012 #3
    Sorry the mass is 2000kg. :)
     
  5. Jun 27, 2012 #4
    For the velocity you can also use F=dp/dt
    [itex]\int_0^t \! f(t) \, \mathrm{d} t. =\int_0^v \! f(mv) \, \mathrm{d} v.[/itex]

    Just find v from acceleration by integral
    Then find d from v by integral too.
     
  6. Jun 27, 2012 #5

    ehild

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    Your initial velocity is -80 instead of zero. Choose other value for k.

    ehild
     
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