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Find expression in terms of time for a particle's velocity?

  1. Jun 14, 2016 #1
    1. The problem statement, all variables and given/known data
    A particle moves along a straight line so that its acceleration t seconds after passing a fixed point O on the line is (2 - 2t) cm/s2. Three seconds after passing O, the particle has a velocity of 5 cm/s. Find and expression, in terms of t, for the velocity of the particle after t seconds.

    2. Relevant equations
    a = dv/dt = d2x/dt2

    3. The attempt at a solution
    From the information, a = -2t + 2 when x = 0, and therefore, by anti-differentiating, v = -t2 + 2t + c.
    I assume that the acceleration of the particle stays at -2t + 2 cm/s2 for the rest of its motion, and so tried substituting (t + 3) in for t to get: -2t - 4, the acceleration of the particle after 3 seconds. Here I got stuck. Do I set up simultaneous equations and eliminate? Have I done my anti-differentiation wrong?

    Any help appreciated,
    Smeato
     
  2. jcsd
  3. Jun 14, 2016 #2

    Ray Vickson

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    Science Advisor
    Homework Helper

    You have a correct antderivative, but from there onwards your logic is wrong. Go back and read again exactly what the question tells you.
     
  4. Jun 16, 2016 #3
    Thanks Ray, it really was a simple question!
    "t seconds after passing O" means that you start counting at zero at the Origin :)

    The correct answer is: v = -t2 + 2t + 8
     
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