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100 meter running with constant acceleration

  1. Nov 5, 2014 #1
    Hello, I am currently by some reason struggling with this problem. I cannot seem to get the correct reasoning here. I would appreciate any help!

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

    Ann and Lisa cross the 100 m finish line at the same time, 10.2 s after start.
    Both had constant acceleration until they reached max speed.
    Ann used 2.0 s to reach max speed.
    Lisa used 3.0 s to reach max speed.
    The max speed was sustained until they reached the finish line.

    1) What was their respective acceleration?
    2) What was their respective max speed?
    3) Who was in the lead after 6.0 s and by how many meters?

    2. Relevant equations

    [itex]v=v_0+at[/itex]
    [itex]x=x_0+v_0t+.5at^2[/itex]
    [itex]v^2=v^2_0+2aΔx[/itex]

    3. The attempt at a solution

    0 = start, 1 = max speed reached, 2 = goal.

    For Ann:
    [itex]t_1=2s [/itex], [itex]t_2=8.2s [/itex], [itex]v_0=0 [/itex], [itex]x_0=0 [/itex], [itex]v_1=v_2 [/itex]

    [itex]v_1=at_1[/itex], [itex]x_1=.5at^2_1[/itex], [itex]v_1t_2=x_2[/itex]

    Here I am struggling, If I do this for both I get 8 unknowns with 6 equations.
     
  2. jcsd
  3. Nov 5, 2014 #2

    ehild

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    Homework Helper
    Gold Member

    You know that Ann used t1=2 s to reach the maximum speed. You also know that the whole time is 10.2 s and the whole distance is 100 m. express v1 and x1 in terms of Ann's acceleration, a. Try to find a from the data given.
    Do the same for Lisa.
     
  4. Nov 5, 2014 #3
    Got it. Thank you! I was to narrow with my thinking, "dumbing" the problem down too much and didn't consider it would have to involve more thinking than just the 3 equations i gave. The fourth I consider was just some rubbish once I checked the dimensions. [itex]v_1t_1+x_1=100 [/itex] was the last one necessary and I was OK. Again, thanks!
     
  5. Nov 5, 2014 #4

    ehild

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    Homework Helper
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    You are welcome :)
     
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