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29 July, 04:28

A certain sprinter has a top speed of 10.5 m/s. If the sprinter starts from rest and accelerates at a constant rate, he is able to reach his top speed in a distance of 12.0 m. He is then able to maintain his top speed for the remainder of a 100 m race. (a) What is his time for the 100 m race

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  1. 29 July, 07:21
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    Total time = 10.667 seconds

    Explanation:

    For the first 12m

    V² = u² + 2as

    10.5² = 0² + 2a (12)

    110.25 = 24a

    a = 4.59375 m/s²

    V = u + at

    10.5 = 0 + 4.59375t

    t = 10.5/4.59375

    t = 2.286 seconds

    For the remaining race

    100-12 = 88m

    He travels at a constant speed for 88m

    S = ut + 1/2 (at²)

    But a = 0

    S = ut

    88 = 10.5t

    t = 88/10.5

    t = 8.38. seconds

    Total time = 2.286 + 8.381

    Total time = 10.667 seconds
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