1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Finding runner acceleration

  1. Jul 14, 2008 #1
    1. The problem statement, all variables and given/known data
    A simple model for a person running the 100 m dash is to assume the sprinter runs with a constant acceleration until reaching top speed, then maintains that speed through the finish line. If a sprinter reaches his top speed of 11.2 m/s in 2.14 s, what will be his total time?

    2. Relevant equations
    Xf = Xi + ((Vx)i)(Delta T) + .5(Ax)(Delta T)^2

    ((Vx)f)^2 = ((Vx)i)^2 + 2(Ax)(Delta X)

    3. The attempt at a solution

    Ok so I need a second opinion to know if I've done this correctly or not. I have the text book answer but I don't know if its correct or not since I'm not getting the same answer.

    I start out by finding the acceleration while the runner gets up to speed.

    11.2 m/s / 2.14 = 5.23 m/s^2

    Using the info given I try and find the distance covered:

    11.2^2 = 0^2 + 2(5.23)(Delta X)

    Delta X = 125.44/10.46 = 11.99 m

    I then find the time taken to cover the distance:

    11.9 = .5(5.23)(Delta T)^2

    (Delta T)^2 = 11.9/2.615 = 4.585
    Delta T = 2.14 s

    OK so now....

    100 m - 11.99m = 88.01m

    I then find the time it takes to travel this distance.

    88.01 = .5(5.23)(delta T)^2

    (delta T)^2 = 33.65

    delta T= 5.80 sec

    so I add the two times

    5.80 sec + 2.14 sec = 7.94 sec

    Am I doing this correctly? My text book is showing me the time as being 10 seconds but I don't see any other way of finding this answer. Any help is appreciated! Thanks!
  2. jcsd
  3. Jul 14, 2008 #2


    User Avatar
    Homework Helper

    Hi osker246,

    The runner is not accelerating once he reaches top speed, so I think this step is not right.
  4. Jul 14, 2008 #3
    wow I cannot believe I over looked that. So then it just comes down to using T= D/R to find the rest of the problem. Thanks A lot alphysicist! I've been stumped on this problem for the past hour trying to figure out where I went wrong.
  5. Jul 14, 2008 #4


    User Avatar
    Homework Helper

    Yes, once you use that equation (T=D/R), the rest looks perfect. And by the way, the way you wrote your original post was great; giving the details of your work made it very easy to understand what you did.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook