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100 Meter Dash

  1. Oct 4, 2007 #1
    A sprinter can accelerate with constant acceleration for 4.0s before reaching top speed. He can run the 100-meter dash in 10s. What is his speed as he crosses the finish line?

    I need help with this problem.

    I know that for the last 6 seconds because he has reached top speed that he has constant velocity. During the first 4 seconds I must use a Uniformed Accelerated Motion formula, and I think I need to actually combine 2 of them together; however, I get an unrealistic answer, like 15m/s, which I know is incorrect.

    Please help me find the sprinter's speed as he crosses the finish line?
     
  2. jcsd
  3. Oct 4, 2007 #2

    Avodyne

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    Science Advisor

    Show us how you got 15m/s. (Which is not crazy, by the way. Since 100m is convered in 10s, the average speed is 10m/s. The speed at the end must be greater than this, since it starts off at zero.)
     
  4. Oct 4, 2007 #3
    Actually I change my answer... 12.5m/s

    But I am still a little skeptical about one step, I actually used another person's related forum to solve some of it and at the part I get stuck I used his/her but I am not quite sure if it is right.

    First
    x= xi + vi(delta t) + .5 a(delta t^2) UAM FORMULA
    x= 0+0+.5a(4^2)
    x= 8a

    Then
    Vf= Vi + a(delta t)
    Vf= 0 + a(4s)

    Therefore 4a= (100-x)6

    And

    4a= (100-x)6
    4a= (100-8a)6 <--this is where I used another source and get confused on the next step
    32a = 100 ?????? is this correct??
    a= 3.125


    Now Final V

    Vf= 4s times 3.125m/s

    Vf = 12.5m/s

    The sprinters speed as he crosses the finish line is 12.5m/s.

    Please Help!!! Is this the correct answer or approach to this problem.
     
  5. Oct 5, 2007 #4

    Avodyne

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    Almost. You've got the 6 on the wrong side in 4a=(100-x)6; it should be (4a)6=100-x, because the velocity is 4a, the time is 6, and you multiply these to get the distance, which is 100-x. With this correct form, you then have 24a=100-x=100-8a, or 32a=100.
    And 12.5m/s is the correct final answer.
     
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