The coordinate of an object is given as a function of time by ${x = 4t}^{2} - {3t}^{3}$ , where x is in meters and t is in seconds. Its average acceleration over the interval from t = 0 to t = 2 s is:

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$4 m / s^{2}$

$- 10 m / s^{2}$

$10 m / s^{2}$

$- 4 m / s^{2}$

answer is C.

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Detailed Solution

$V = \frac{d x}{d t} = 8 t - 9 t^{2} At t = 0 s V_{1} = 0 m / s At t = 2 s V_{2} = - 20 m / s a_{av} = \frac{V_{2} - V_{1}}{Δt} = \frac{- 20 - 0}{2} = - 10 m / s^{2}$

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