According to the law of motion, the move of a particle is explained by s = f(t) where s represents the position of the particle and t represents the time. Consider the following equation f(t) = t3 − 12t^2 + 36t where t is measured in seconds and s is measured in feet. (a) When is the particle at rest? (b) Find the displacement of the particleduring the time period, 1

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According to the law of motion, the move of a particle is explained by s = f(t)
where s represents the position of the particle and t represents the time.
Consider the following equation f(t) = t3 − 12t^2 + 36t where t is measured in seconds and s is measured in feet.

(a) When is the particle at rest?

(b) Find the displacement of the particleduring the time period, 1<t<4. Give an interpretation to yhe answer obtained.

(c) Find the total distance travelled during the first 8 seconds.

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