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Instantaneous Velocity Car Problem

  1. Sep 18, 2010 #1
    A car is stopped at a traffic light. It then travels along a straight road so that its distance from the light is given by x(t)= bt^2 -ct^3, where b = 2.40m/s^2 and c = 0.120 m/s^3. How do you calculate the average velocity of the car for the time interval t=0 to t=10.

    I think that maybe I need to take the derivative of the equation but then what please help!
  2. jcsd
  3. Sep 18, 2010 #2


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    Hello mopar969,
    If you only need to find the average velocity, simply calculate the total distance traveled, divided by the time it takes to get there.
  4. Sep 18, 2010 #3
    Thank you. I cant believe that it was that simple. I was thinking instantaneous velocity that is why I was thinking about taking its derivative.
    However, the question has another part to it that I am stuck on it says:

    How long after stating from rest is the car again at rest? Please Help and Thanks.
  5. Sep 18, 2010 #4
    You're searching the time t when the velocity is 0.

    x(t)= bt^2 -ct^3, this finds the displacement as a function of time. You'll need another equation (related to this one) to find the velocity as a function of time.
  6. Sep 18, 2010 #5
    Would I need the derivative of the displacement function?
  7. Sep 18, 2010 #6
    Yes that would give you the velocity.
  8. Sep 18, 2010 #7
    My next problem is how do I get t by itself?
  9. Sep 18, 2010 #8
    Never mind I realized that I could use the quadratic formula.
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