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Applications of Piecewise Linear Functions and Integrals : Velocity, Time and Acceleration

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A car is traveling on a straight road with velocity 55 ft/sec at time t = 0. For 0 ≤ t ≤ 18 seconds, the car's acceleration a(t) , in ft/sec2, is the piecewise linear function defined by the graph above.
(a) Is the velocity of the car increasing at t = 2 seconds? Why or why not?
(b) At what time in the interval 0 ≤ t ≤ 18, other than t = 0 is the velocity of the car 55 ft/sec? Why?
(c) On the time interval 0 ≤ t ≤ 18, what is the car's absolute maximum velocity, in ft/sec, and at what time does it occur? Justify your answer.
(d) At what times in the interval 0 ≤ t ≤ 18, if any, is the car's velocity equal to zero? Justify your answer.

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Velocity, Time and Acceleration are investigated using integration. The solution is detailed and well presented.

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