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Rocket car kinematics

  1. Dec 12, 2014 #1
    1. The problem statement, all variables and given/known data
    A "rocket car" is launched along a long straight track att = 0 s. It moves with constant acceleration a1 = 2.9m/s2 .At t = 2.8s , a second car is launched with constant acceleration a2 = 7.0m/s2 .

    At what time does the second car catch up with the first one?
    How far down the track do they meet?

    2. Relevant equations
    [itex]v_f^2 = v_i^2 + 2a(Δx)[/itex]
    [itex]v_f = v_i + at[/itex]
    [itex]x_f = x_i + v_it + 1/2at^2[/itex]

    3. The attempt at a solution
    [itex]x_f = (1/2)(2.9m/s^2)(2.8s)^2 = 11.368m[/itex]

    Car 1's X initial is 11.368m when the second car is launched.

    Equation for X final of car 1:
    [itex]x_f = (0.5)(2.9m/s^2)(t)^2 + (8.12m/s)(t) + 11.368m[/itex]

    Equation for X final of car 2:
    [itex]x_f = (0.5)(7.0m/s^2)(t)^2[/itex]

    Setting X final equal to each other (when second car meets up with first one)
    [itex](0.5)(7.0m/s^2)(t)^2 = (0.5)(2.9m/s^2)(t)^2 + (8.12m/s)(t) + 11.368m[/itex]
    [itex] t = 5.06s[/itex]

    It turns out 5.06s is incorrect. Not sure what I am doing wrong here. Just figured out how to use the fancy math notation! My post is a well-crafted scientific paper.
     
  2. jcsd
  3. Dec 12, 2014 #2

    mfb

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    2016 Award

    Staff: Mentor

    I can confirm your answer, assuming both cars start from the same place.

    Edit: Ah, jbriggs found the problem, your answer is not the final answer yet.
     
    Last edited: Dec 12, 2014
  4. Dec 12, 2014 #3

    jbriggs444

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    Science Advisor

    First thing to do is to double-check your answer.

    After 2.8 + 5.06 seconds at 2.9 m/sec^2, where is car number 1?
    After 5.06 seconds at 7 m/sec^2, where is car number 2?

    Second thing to do is to make sure you are answering the right question. Where does t=0 occur in the problem statement? Where does t=0 occur in your final formula?
     
  5. Dec 13, 2014 #4
    I got the answer. I realized that 5.06s is the time after the release of the second car where they meet - not after the release of the first car. I just added 2.8s to 5.06s and got the correct answer: 7.9s.

    Thanks for the help!

    Then I just plugged values back in to get the answer to the second part, 90m.
     
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