How to determine the total time of a runner if time is given for only a fraction of the entire race?

The runner's acceleration is constant. He covers the last 1/9 of the race in 6 seconds. How long does it take him to run the entire race?

I am stuck because there is such little information. I am not given the total distance, acceleration, or final velocity.

Using the position formula x=x(i)+v(i)t+1/2(a)(t^2) I find that t=sqrt(2x/a).

If I differentiate the function, then f'(t)=at, which gives the instantaneous velocity at t.

I'm not sure how to tackle this problem.

2 Answers

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  • Aenima
    Lv 6
    8 years ago
    Favorite Answer

    You'll need to find equations that link the states between the last 1/9 distance of the race, the first 8/9 and the total length together.

    We aren't given a distance, but call the total distance L or D.

    For the first 8/9 ths you can use, vf^2 = v0^2 + 2a(x-x0)

    Vf here would correspond to the initial speed between the last 1/9 of the length.

    Vf = v0 + at

    And you can use the first equation again but for the entire length:

    Vff^2 = v0^2 + 2a(x-x0)

    You can solve for acceleration with all these and then for total time using:

    X = x0 + v0t + .5at^2 for the entire race.

    I tried it myself and it was a bit challenging with all the algebra. But I got a final answer of 104.9 seconds. Is the answer given?

  • 4 years ago

    That is gonna be like spinning the bottle to peer who will get the crown, I say which ever one has the most fanatics from R/S. Every person there seems to have it out for the each of ya.~~Peace~~

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