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Simple Equation

  1. Sep 2, 2010 #1
    1. The problem statement, all variables and given/known data

    A car of mass m has an engine which can deliver power P. What is the minimum time in which the car can be accelerated from rest to a speed v?

    2. The attempt at a solution

    P = W/t
    (W is work done, t is time)

    F = ma

    P = Fs/t
    (F is force, s is distance)
    P = mas/t
    Making t as the subject,
    t = mas/P
    t = mv2/P

    Is there any thing wrong with my final equation?
  2. jcsd
  3. Sep 2, 2010 #2


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    I am missing a factor of 1/2. Probably you forgot to take an average somewhere...
    An easier way might be from an energy consideration: the amount of work that the engine needs to do, is at least the added kinetic energy, right?
  4. Sep 4, 2010 #3
    If I use kinetic energy, instead of work done,

    then the equation becomes:

    t = mv2/2P

    Which is the correct answer then? And what factor 1/2?
  5. Sep 5, 2010 #4


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    Exactly. Note that there is an extra 2 in the denominator now. That's the factor of 1/2 I am talking about.

    (By the way, it is not "instead of work done"... the kinetic energy is precisely the work done. You meant, "instead of forces" :))
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