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Mechanics problem question

  1. Feb 15, 2015 #1
    1. The problem statement, all variables and given/known data
    A truck starts from rest and accelerates at 0.9m/s2. 0.8s later, a car accelerates from rest at the same starting point with an acceleration of 2.5m/s2

    Where and when does the car catch the truck?


    2. Relevant equations
    Motion equations

    Xf-Xo=Vox(t)+1/2(a)(t)^2

    3. The attempt at a solution

    x truck=x car

    1/2(a)(t)^2=1/2(a)(t-0.8s)^2
    1/2(a)(t)^2=1/2(a)(t^2-1.6t+0.64)
    1/2(0.9)t^2=1/2(2.5)(t^2-1.6t+0.64)
    0.45t^2=1.25t^2-2t+0.8
    0.8t^2-2t+0.8t=0
    quadratic equation =

    2+1.2/1.6=2s
    2-1.2/1.6=0.5s

    I don't know where I went wrong but the value for time isn't working for me. The assignment continues to say the answer is incorrect... Please help me pin point my error so I can correct myself.

    Thank you

     
  2. jcsd
  3. Feb 15, 2015 #2
    I would try to redo the algebra. Perhaps cancel out 1/2 on both sides to make things less messy

    Edit: your math looks right. Plug in 2s into the equation, it works. Now plug in .5s, hopefully you notice something.

    Always check your answer to see if they make mathematical sense and physical sense.
     
    Last edited: Feb 15, 2015
  4. Feb 15, 2015 #3
    I already canceled them out and still got the same results.... It doesn't work still.
     
  5. Feb 15, 2015 #4
    Hey, do you know how this equation is derived? If you work this in the integral form you might see what you did wrong.
     
  6. Feb 15, 2015 #5
    The thing is we didn't learn integral form yet so I don't know how I would do it.
     
  7. Feb 15, 2015 #6
    Well, ok.

    Judging from your work, it seems as if you wanted to keep the time constant with respect to the first car to start. There's nothing wrong with this. However, if this is the case, your work is saying that the two cars will be meeting each other at different times with respect to the first car. Namely, you are saying that car 2 is going to come in contact with the first car .8 seconds earlier than car 1 comes in contact with car 2. How could they come in contact at different times? They should come in contact at the exact same ending time T.
     
  8. Feb 15, 2015 #7
    How could I set the equation in that case? should I set both cars (t-0.8)^2?
     
  9. Feb 15, 2015 #8
    Ill just ask my teacher tomorrow, thank you guys.
     
  10. Feb 15, 2015 #9
    It looks correct actually
     
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