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18 March, 19:00

Over a short interval the coordinate of a car in the meters isgiven by x (t) = 27t - 4.0 t3 where time t is in seconds, at the end of 1.0s the acceleration of the car is

1. 27 m/s2

2. 4.0 m/s2

3. - 4.0 m/s2

4. - 12 m/s2

5. - 24 m/s2

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Answers (1)
  1. 18 March, 22:18
    0
    5. - 24 m/s²

    Explanation:

    Acceleration: This can be defined as the rate of change of velocity.

    The S. I unit of acceleration is m/s².

    mathematically,

    a = dv/dt ... Equation 1

    Where a = acceleration, dv/dt = is the differentiation of velocity with respect to time.

    But

    v = dx (t) / dt

    Where,

    x (t) = 27t-4.0t³ ... Equation 2

    Therefore, differentiating equation 2 with respect to time.

    v = dx (t) / dt = 27-12t² ... Equation 3.

    Also differentiating equation 3 with respect to time,

    a = dv/dt = - 24t

    a = - 24t ... Equation 4

    from the question,

    At the end of 1.0 s,

    a = - 24 (1)

    a = - 24 m/s².

    Thus the acceleration = - 24 m/s²

    The right option is 5. - 24 m/s²
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