A particle moves according to a law of motion s = f(t), t ? 0, where t is measur

Question

A particle moves according to a law of motion s = f(t), t ? 0, where t is measured in seconds and s in feet. f(t) = t3 ? 15t2 + 72t (d) When is the particle moving in the positive direction? (Enter your answer in interval notation.) (e) Find the total distance traveled during the first 7 s. (f) Find the acceleration at time t. (G) Find the acceleration after 5 s. (h) When is the particle speeding up? (Enter your answer in interval notation.) When is it slowing down? (Enter your answer in interval notation.)

Explanation / Answer

FOLLOW THIS Velocity is defined as the rate of change in position in a specific direction. These are the three components of velocity, rate of change, change in position and direction. The rate of change in position of an object is actually the speed. We can therefore say that velocity is speed in a particular direction. Any activity lacking one of the two components will always result in zero velocity. Due to the direction component of velocity it is considered a vector quantity. These are quantities that have magnitud

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