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Constant Acceleration

  1. Sep 19, 2006 #1
    I was wondering if anyone could help me with part b of this question.

    You are arguing over a cell phone while trailing an unmarked police car by 28m; both your car and the police car are traveling 110km/h (about 31m/s). You take your eye off the road for 2.0s because of the argument. At the very beginning of the 2.0s, the police car brakes at 5m/s^2.

    a) what is the separation between the two cars when your attention returns?

    I already got this right, its 18 meters.

    b) Suppose you take another .40s to realize the danger and begin braking. If you too brake at 5m/s^2, what is your speed when you hit the police car?

    For this I have solved for the velocity of the police car after it has been braking for 2.4s (15.7778 m/s). The velocity of my car is still 27.7778m/s. And the seperation distance is now 14.3999m after the 2.4 s.

    I am confused on where to go at this point with the question.

    If anyone could help me that would be great.

  2. jcsd
  3. Sep 19, 2006 #2


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    Staff: Mentor

    Now solve for the delta-t until impact, then plug that delta-t back into the velocity equation.
  4. Sep 19, 2006 #3
    I calculated that the police car takes 3.15556 seconds to stop from the instant that you start braking. That equals a total of 24.8938m + the speration distance of 14.3999m= 39.293797.

    Therefore, you have 39.293797m to brake at a rate of 5 m/s^2.

    I then solved this to find the car to have a velocity of 19.459398 m/s which equals 70.05383 km/h.

    Is this correct?
  5. Sep 19, 2006 #4


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    Staff: Mentor

    I haven't been following the numbers well enough to be able to say if it's correct, but it looks reasonable. I'd suggest drawing a graph to help you double-check your work. Draw a graph of distance versus time, and plot two lines for the two cars. Start with the initial separation info and velocities, and plot out their position over the course of each part. The crash happens when the two position lines meet. You can also make a separate plot of velocity versus time if that helps. Gotta go. Good work.
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