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A runner is at the starting gate and hears the starting gun. He begins running with a constant acceleration ai = 0.55 m/s2. He crosses the finish line at d = 100 m and then begins slowing down. It takes him tr to cross the finish line. It takes him ts = 6.5 s to return to rest after crossing the finish line. For this problem, use a coordinate system with the runner is moving in the positive direction.

Randomized Variables
ai = 0.55 m/s2
ts = 6.5 s
show answer No Attempt 33% Part (a) Find an expression for the time it takes for the runner to cross the finish line, tr, from the start in terms of d and ai.

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  1. during the run:
    vf^2=vi^2 + 2ad solve for vf

    but vf= ai*t solve for time t.
    so sqrt (2ad)=ai*t
    square both side
    2ad=a^2 t^2
    t= sqrt (2d/a)

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    bobpursley

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