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2 November, 14:25

A world-class sprinter can burst out of the blocks to essentially top speed (of about 11.5 m/s) in the first 15.0 m of the race. what is the average acceleration of this sprinter, and how long does it take her to reach that speed?

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  1. 2 November, 14:43
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    Given:

    u = 0, initial speed (sprinter starts from rest)

    v = 11.5 m/s, final speed

    s = 15 m, distance traveled to attain final speed.

    Let

    a = average acceleration,

    t = time taken to attain final speed.

    Then

    v² = u² + 2as

    or

    (11.5 m/s) ² = 2 * (a m/s²) * (15 m)

    a = 11.5² / (2*15) = 4.408 m/s²

    Also

    v = u + a t

    or

    (11.5 m/s) = (4.408 m/s²) * (t s)

    t = 11.5/4.408 = 2.609 s

    Answer:

    The average acceleration is 4.41 m/s² (nearest hundredth).

    The time required is 2.61 s (nearest hundredth).
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