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Lamborghini Speed test Calculations

  1. Mar 12, 2012 #1
    1. The problem statement, all variables and given/known data

    A lamborghini's breaking speed is 6.7 times that of its acceleration. The total time taken to go from 0 to 100 and back to 0 is 13.7 seconds. What is the displacement of the car?


    2. Relevant equations
    Unsure at the moment


    3. The attempt at a solution

    So, you devide the treck into 2 parts: Acceleration and Breaking

    Acceleration:
    a= x
    t= y
    d= ?
    Vo = 0
    Vf = 100

    Breaking:
    a= -6.7x
    t= 13.7 - y (y being the accelerating time)
    Vo= 100
    Vf = 0
    d=?

    Honestly im unsure as to what to do :S, any help would be much appriciated.
     
  2. jcsd
  3. Mar 12, 2012 #2

    SammyS

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    Is this the wording given to you ???

    "Braking speed" ? "Braking speed" ? "Braking speed" ? "Braking speed" ?

    (I'll get off of that soap-box!)

    First find the forward acceleration.

    How are acceleration, change in velocity and time all related ?
     
  4. Mar 12, 2012 #3

    Nugatory

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    Staff: Mentor

    With what you have already, you can calculate how much time the car spent accelerating from zero to one hundred and decelerating from one hundred to zero.

    These times, and the change in speed which you already know, will give you the acceleration and deceleration.

    Finally, there's an equation that gives you the distance covered in a given time at a given acceleration/deceleration, and that will take you to the answer.

    As a historical note: 427 Cobras were doing zero to one hundred to zero in under ten seconds, more than forty years ago. Of course you would have to be totally completely barking mad, and suicidal as well, to push one of those cars to those limits... No ABS, no launch control, no traction control....
     
  5. Mar 12, 2012 #4
    Ya sorry, its braking acceleration :P. Anyway, Acceleration, Velocity and Time are related through the 4 big kinematic formulas:

    V= Vo+ at
    D = 1/2(v+Vo) * t
    d = Vo*t + 1/2at^2
    V^2 = Vo^2 + 2ad

    Correct?

    This is what ive come up with, might be absolutely wrong :S, sorry, JUST started physics:

    1a + 6.7a = 13.7 sec
    7.7a = 13.7 sec
    a = 1.78

    1.78 * 6.7 = 11.92 sec

    11.92 + 1.78 = 13.7 sec

    So it takes 11.92 seconds to accelerate, then 1.78 to get back to 0.

    Then, using d = 1/2(V+Vo) * t

    100 mph = 44.704 m/s

    d = 1/2(44.704 + 0) * 11.92
    d= 22.352 * 11.92
    d= 266.43 m

    Using it again:

    d= 1/2(0 + 44.704) * 1.78
    d= 22.352 * 1.78
    d=39.78 m

    266.43 m + 39.78 m = 306.22 m

    Did I do it right or did I botch the entire thing?

    EDIT: Nugatory, thats what ive done here (or tried to do :P). And Cobras are beauty cars, my friends dad actually has a Shelby Cobra, such an amazing car :)
     
    Last edited: Mar 12, 2012
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