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Math Help - Motion problem. Acceleration with respect to displacement

  1. #1
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    Motion problem. Acceleration with respect to displacement

    Im having a problem solving a physics related problem. This is it:
    A truck travels at a speed of 4m/s along a circular road with radius if 50m. For a short distance, from s=0, its speed is then increased by a(tan) = (0.05s) m/s, where s is in meters. Determine the speed at s=10.

    I thought this was a simple integration to find velocity, but i realized that i cant just integrate with respect to s.There is no time in this problem. So from there, I have no idea what to do really. It is hard for me to visualize this sort of equation. And just to note, a is tangential acceleration. The answer is 4.58 m/s. I just cant get that answer.
    Any help is appreciated, thanks!

    Chris
    Last edited by chrsr345; February 9th 2008 at 05:20 PM.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by chrsr345 View Post
    Im having a problem solving a physics related problem. This is it:
    A truck travels at a speed of 4m/s along a circular road with radius if 50m. For a short distance, from s=0, its speed is then increased by a = (0.05s) m/s, where s is in meters. Determine the speed at s=10.
    Please repost this using the wording in the actual problem.

    RonL
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  3. #3
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    That is the wording in the actual problem. it also asks for the magnitude of acceleration after it asks for velocity at s=10. But i can easily find that once i find the velocity. But yes, those are the words.
    Like i stated, the accel given is the tangential a, or a-sub-t.

    Ive asked a friend who has taught upto diff equations and even he didnt know how to do it
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  4. #4
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    The only forumla i have that even relates to this is a(tan)ds = v dv
    So i integrated both sides and got 0.025s^2. at s = 10, i get 2.5m/s + 4m/s = 6.5m/s: Wrong!

    Im at a dead stop here.
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  5. #5
    ra2warroom
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    use ads = vdv

    int=integral

    int(.05s)ds = int(v)dv

    (.05s^2)/2 = (v(final)^2 - v(initial)^2)/2

    plug in 10 and get v(final) = 4.58m/s
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