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Help with a 1-dimention kinematics question

  1. May 24, 2007 #1
    1. The problem statement, all variables and given/known data
    setting a new world record in a 100m race, maggie and judy cross the finish line in a dead heat, both taking 10.2s. Accelerating uniformly, maggie took 2.0s and judy 3.0s to attain maximum speed, which they maintained for the rest of the race. (a) what was the acceleration of each sprinter?

    2. Relevant equations


    3. The attempt at a solution

    tried using the 2nd equation listed to get the distance which i would then factor into the first equation ... and dealing with multi variables.. things got very messy from here... i ripped apart 3 pages from my notebook already so some help would be highly appreciated.
  2. jcsd
  3. May 24, 2007 #2

    Doc Al

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    Staff: Mentor

    Realize that each sprinter's motion has two segments: (1) acceleration from rest to final speed, and (2) constant speed motion at the final speed. The times for these segments, as well as the total distance, are provided.
  4. May 24, 2007 #3


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    Yes this is a bit fiddly but you have to consider the question in two parts. The first part is when the runners are accelerating and the second is when they are travelling at constant speed.

    The maximum speed reached after acceleration is thus [tex] v=a{t_1}^2[/tex]

    and the distance travelled is [tex] s=\frac{1}{2} a t_1^2 [/tex]

    The distance travelled during the second part can be worked out and thus when you add the distances together you know they should make 100 and you can solve for a.
    Last edited: May 24, 2007
  5. May 24, 2007 #4
    For each runner split the motion into two sections. One with uniform acceleration and one with no acceleration.

    The equations you mention only apply to the motion of the runners while they accelerate. When they reach maximum velocity the only equation necessary is


    where x is the distance traveled while at max vel, vf is the max velocity achieved after accelerating and t is the time left after accelerating.

    This distance plus the distance traveled while accelerating (use your first equation with xi and vi =0) adds up to 100m.
    This fact should give you an equation with a and vf as unknowns. Using vf=vi+at with vi=0 you can remove vf and replace it with at, where t is the time the runner accelerated for. Now solve for a.
  6. May 26, 2007 #5
    thanks for your help guys, and yes i did know that i have to solve it at 2 parts... but i couldn't solve it with either part. Thanks for your help guys. I understand it now :)
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