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First derivative problem

  1. Jun 4, 2014 #1
    A Car, initially travelling at the speed 100 km/h, slows down according to the formula. L(t)= At - Bt^2
    Where L is the travelled distance, t is the time & B= 90 km/h^2. Using derivative, find the time moment when the car speed becomes 10 km/h. Find the acceleration of the car at this moment.

    i think this is a function (my interpretation below)

    50(t)= 100t - 90t^2

    would i just have to graph the function?

    any guidance appreciated
    Last edited: Jun 4, 2014
  2. jcsd
  3. Jun 4, 2014 #2


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    That formula for L(t) is reminiscent of a constant acceleration motion. So you can find the negative acceleration of the car by inspection (since you know B).

    Why is there a 50t on the LHS of your equation?

    What definitions of velocity and acceleration do you have? In particular, ones relating to position?
  4. Jun 4, 2014 #3
    The car has a velocity of 100km/h and slows down to 10km/h?

    The 50 was just a random distance number. Disregard it.
  5. Jun 4, 2014 #4


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    Yes. You can think of the situation as the car applying brakes and decelerating at a constant rate.
  6. Jun 4, 2014 #5
    Do you know where i could do some reading to find out where to begin with this problem?
  7. Jun 4, 2014 #6


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    Do you have an introductory physics textbook? E.g see the first few chapters of Halliday, Resnick, Walker.

    Related links:
    Section 1 and 3.1 of http://en.wikipedia.org/wiki/Acceleration

    If you want to understand things well though, nothing beats a good textbook and the accompanying problems.
  8. Jun 4, 2014 #7
    If you know calculus, then the first derivative of distance is velocity, and the second derivative is acceleration.
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