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Math Help - Help with Mechanics - Distance Travelled

  1. #1
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    Help with Mechanics - Distance Travelled

    Hi all,

    I have the following question but I'm not sure where to start?

    - A particle travels, starting with initial speed u, with uniform acceleration a. Show that the distance travelled during the nth second is u+an-1/2a.

    Does anyone have any idea how to do this? Any help would be greatly appreciated!

    Thanks,
    Ronan
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by ronan116 View Post
    Hi all,

    I have the following question but I'm not sure where to start?

    - A particle travels, starting with initial speed u, with uniform acceleration a. Show that the distance travelled during the nth second is u+an-1/2a.

    Does anyone have any idea how to do this? Any help would be greatly appreciated!

    Thanks,
    Ronan
    You should know that starting from s=0 the position of the particle after t seconds with these assumptions is:

     <br />
s(t)=\frac{at^2}{2}+ut<br />

    Then the distance moved in the n th second is:

     <br />
d(n)=s(n)-s(n-1)<br />

    CB
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  3. #3
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    Thanks I get the first part but how did you get from there to the second part?
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  4. #4
    Grand Panjandrum
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    Quote Originally Posted by ronan116 View Post
    Thanks I get the first part but how did you get from there to the second part?
    At the start of the n-th second the position is s(n-1) at the end of the n-th second the position is s(n) and as the particle is always moving in the same direction the distance traveled in the n-th second is the difference of the two positions

    CB
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  5. #5
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    Ok, I get why the distance travelled would be s(n) - s(n-1) but how does that give me the equation u+an-1/2a?

    Thanks for all your help
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