Position Velocity and Acceleration



Integral Applications

You may use a calculator for both problems. Show all of the necessary work.

Use proper mathematical notation.

2001 AB3

A car is traveling on a straight road with velocity 55ft/sec at time t=0. For [pic] seconds, the car’s acceleration a(t), in [pic], is the piecewise 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 [pic], other than t=0, is the velocity of the car 55ft/sec? Why?

c) On the time interval [pic], what is the car’s absolute maximum velocity and at what time does it occur? Justify your answer.

d) At what times in the interval [pic], if any is the car’s velocity equal to zero? Justify your answer.

2. The electrical power consumption (measured in kilowatts) at a factory t hours after midnight during a typical day is modeled by [pic].

a) What is the electrical consumption of the factory at 10 am?

b) What is the electrical consumption of the factory at 2 pm?

c) What is the total kilowatt-hours of electrical energy consumed by the factory in a typical 24 hour day?

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