A car accelerates uniformly from rest and reaches a speed of 21.9 m/s in 8.99 s. Assume the diameter of a tire is 57.5 cm. (a) Find the numb

Question

A car accelerates uniformly from rest and reaches a speed of 21.9 m/s in 8.99 s. Assume the diameter of a tire is 57.5 cm. (a) Find the number of revolutions the tire makes during this motion, assuming that no slipping occurs.

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Đan Thu 5 years 2021-08-29T09:40:12+00:00 1 Answers 17 views 0

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  1. nguyetanh
    0
    2021-08-29T09:41:34+00:00
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    Answer:

    Explanation:

    initial velocity, u = 0 m/s

    time, t = 8.99 s

    final velocity, v = 21.9 m/s

    diameter of tyre, D = 57.5 cm

    (a) Let a is the acceleration, and n be the number f revolutions made by the tyre.

    Use first equation of motion

    v = u + at

    21.9 = 0 + a x 8.99

    a = 2.44 m/s²

    Use third equation of motion

    v² = u² + 2 a s

    21.9 x 21.9 = 0 + 2 x 2.44 x s

    s = 98.28 m

    Circumference of wheel, S = π x D = 3.14 x 0.575 = 1.8055 m

    number of revolutions, n = distance / circumference

    n = 98.28 / 1.8055

    n = 54.4

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