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8 October, 03:26

Position coordinate of a particle confined to

move along a straight line is given by s=

2t

3-24t + 6, where s is measured in meters

from a convenient origin and t is in seconds.

Determine: (a) time required for the particle

to reach a velocity of 72 m/s from its initial

condition at t = 0, (b) acceleration of the

particle when v = 30 m/s, and (c) net

displacement of the particle during the

interval from t = 1 s to t = 4 s.

+2
Answers (1)
  1. 8 October, 03:44
    0
    a) 4 s

    b) 36 m/s²

    c) 54 m

    Explanation:

    s = 2t³ - 24t + 6

    a) Find t when v = 72 m/s.

    v = ds/dt

    v = 6t² - 24

    72 = 6t² - 24

    6t² = 96

    t = 4

    b) Find a when v = 30 m/s.

    a = dv/dt

    a = 12t

    When v = 30:

    30 = 6t² - 24

    6t² = 54

    t = 3

    a = 36

    c) Find Δs between t = 1 and t = 4

    Δs = (2 (4) ³ - 24 (4) + 6) - (2 (1) ³ - 24 (1) + 6)

    Δs = 38 - (-16)

    Δs = 54
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