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Homework Help: Differentiation car problem

  1. Dec 7, 2007 #1
    1. The problem statement, all variables and given/known data
    A car, travelling at a speed of 90km/h, approaches a stop sign 40m ahead. If the car immediately begins to decelerate at a rate of -8m/s^2, will it be able to stop in time? Justify your response

    2. Relevant equations
    d = 1/2at^2 + vt

    3. The attempt at a solution

    I found time by doing t = v/a and found it to be 25/8s
    Then I subbed it in d = 1/2at^2 + vt and got an answer of 39.1m, which is smaller than 40m. So it will be able to stop in time.
    But this assignment is all about differentiation, so I should be finding a derivative somewhere.... but I don't know where to find a derivative to solve this problem!!
    Please help~~
  2. jcsd
  3. Dec 7, 2007 #2

    Well, you've kind of already used differentiation, but you may not know it. You have an equation for position:

    [tex] x(t) = x_0 + v_0t + \frac{1}{2}at^2 [/tex]

    The velocity is found by taking the derivative of this equation:

    [tex] v(t) = \frac{dx}{dt} = v_0 + at [/tex]

    So when you calculated your time (where did you get t = v/a?) you were using this equation.

    Hope this helps.
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