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Finding the displacement of a braking car, with limited variables.

  1. Nov 7, 2009 #1
    1. The problem statement, all variables and given/known data
    A car is travelling at 120km/h when it slams on the brakes. How long is the skid mark if the coefficient of friction is 0.62?(hint: convert km/h to m/s)

    Given: initial velocity: 33.3m/s; final velocity: 0m/s; coefficient of fricition: 0.62

    2. Relevant equations
    μ = Ffriction/Fnormal; a= Force/mass

    3. The attempt at a solution
    Because of the absense of a time value, i'm finding it very difficult to use and displacement equation i've been given. I understand the the change in velocity (after being conversted to m/s) is 33.33m/s, but thats as far as i've gotten.

    I was wondering is anyone could help me derive some other variable: such as the change in time, or the acceleration, with the given data.
     
  2. jcsd
  3. Nov 8, 2009 #2

    tiny-tim

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    Welcome to PF!

    Hi Symon! Welcome to PF! :smile:

    Is the "displacement equation" work done = force times (or "dot") displacement?

    If so, you don't need the time. :wink:
     
  4. Nov 8, 2009 #3
    Thus far, i am unfamiliar with that equation, here are some of the equations that I've either derived or have been given:

    1) ∆d=〖(∆v)〗^2/2a
    2) ∆d= ∆v∆t
    3) ∆d=vi∆t+ 1/2 a〖(∆t)〗^2

    As you can see, the first equation that i have neglects time, but i am unable to use it without finding the acceleration (which is another equation i need time for). Is there some alternate way i can find the acceleration, force involved, time, or mass?
     
  5. Nov 8, 2009 #4

    tiny-tim

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    ok … you're using the usual constant acceleration equations.

    (but #1 is wrong … it should have ∆(v2), not (∆v)2, and #2 is completely wrong … replace it with ∆v = a∆t)

    Yes, you can find the acceleration, a, by starting with the friction coefficient, µ = 0.62 …

    that will give you the force, and then you can find the acceleration from good ol' Newton's second law. :wink:
     
  6. Nov 8, 2009 #5
    Thank you :)
     
    Last edited: Nov 8, 2009
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