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Suvat - Two cars approach each other on a straight road

  1. Aug 8, 2012 #1
    Suvat -- Two cars approach each other on a straight road

    1. The problem statement, all variables and given/known data

    Two cars approach each other on a straight road. Car A is moving at 16m/s and car B at 8m/s. When they are 45m apart both drivers apply their brakes. Car A slows down at a rate of 2m/s^2 while car B slows down at 4m/s^2. Where and when do the cars collide?

    2. Relevant equations

    I'm assuming that this would result in a simultaneous equation given that there are two unknowns; distance (s) and time (t) (where and when).

    3. The attempt at a solution

    CAR A
    s = s
    u = 16m/s
    v = x
    a = -2m/s^2
    t = t

    s = ut + 1/2 at^2
    s = 16t - t^2
    Equation 1

    CAR B
    s = s
    u = 8m/s
    v = x
    a = -4m/s^2
    t = t

    s = ut + 1/2 at^2
    s = 8t - 2t^2
    Equation 2

    Equation 1: s = 16t - t^2
    Equation 2: 2s = 16t - 4t^2

    It is at this point I fall as I still land up with two unknown variables: -s = 5t^2

    Where am I going wrong?
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Aug 8, 2012 #2
    Re: Suvat

    Let the distance traveled by car A before collision be sA and that by car B be sB. The total distance sA + sB should be 45 (why?).

    Now write sA and sB in terms of t and simplify.
     
  4. Aug 8, 2012 #3

    gneill

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    Staff: Mentor

    Re: Suvat

    Be sure to check the velocities of each car at the calculated time of collision. Why? Because you need to make sure that the result you obtain is physically meaningful in the context of the problem.
     
  5. Aug 8, 2012 #4
    Re: Suvat

    Your equations imply that both cars moving in same direction and start to slow down at same location where t=0, s=0 for both.
    At t=0 they are 45m apart and opposite direction.

    One of the equations is correct, say car A.
    The other ,car B, should have value at t=0, s=45m.
    As they approach each other, car A should have increasing distance from origin(until it starts to reverse) and car B decreasing value until it starts reversing too.
     
    Last edited: Aug 8, 2012
  6. Aug 9, 2012 #5
    Re: Suvat -- Two cars approach each other on a straight road

    I think I get it now. Are the answers;
    t = 3s and s = 39m
     
  7. Aug 9, 2012 #6

    gneill

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    Staff: Mentor

    Re: Suvat -- Two cars approach each other on a straight road

    Did you check the velocities of the two cars at this time of impact?
     
  8. Aug 9, 2012 #7
    Re: Suvat -- Two cars approach each other on a straight road

    should they be the same?
     
  9. Aug 9, 2012 #8

    gneill

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    Staff: Mentor

    Re: Suvat -- Two cars approach each other on a straight road

    What do you think? Hint: Are you sure that BOTH cars will still be moving at the time of collision? Is it possible for one car to come to a halt (from braking) before the other?
     
  10. Aug 9, 2012 #9
    Re: Suvat -- Two cars approach each other on a straight road

    http://img684.imageshack.us/img684/6497/collidingcars2.jpg [Broken]
    http://img36.imageshack.us/img36/5285/collidingcars.jpg [Broken]

    It is a piecewise function not purely parabolic function.
    Both have maximum distance travelled. No reversing.
    Thanks gneill, it's really tricky question.
     
    Last edited by a moderator: May 6, 2017
  11. Apr 5, 2013 #10
    What is car B's velocity after 2s?
     
  12. Apr 6, 2013 #11

    PeterO

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    Homework Helper

    Did you check to see if the cars actually collide at all.

    How far will Car A have travelled by the time it stops, if Car B didn't exist.
    How far will Car B travel before it stops, if Car A didn't exist.

    If those two distances total less than 45m, the cars simply stop.

    Which car would have stopped first?

    Would that car have stopped before the other collided with it? (if there was a collision)
     
  13. Oct 22, 2017 at 9:43 PM #12
     
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