A particle moves according to a law of motion s ft t3, Mathematics

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A particle moves according to a law of motion s ft t3

A particle moves according to a law of motion s = f(t) = t³ -9t²+24t, t ≥ 0, where t is measured in seconds and s in feet,

Find the velocity at time t.

What is the velocity after 4 s?

When is the particle at rest?

When is the particle moving in the positive direction?

Find the total distance traveled during the first 6 s.

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Mathematics: A particle moves according to a law of motion s ft t3

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