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AP Calculus Problem Set 501/25/12

Upon completion, circle one of the following to assess your current understanding:

Completely understand / Mostly understand / Sort of understand / Don’t understand

1) Brian rides his unicycle to school, starting at home at minutes and arriving at school at . During the time interval, , his velocity, , in miles/minute, is modeled by the piecewise-linear function whose graph is shown below.

a)Find the acceleration, if it exists, of Brian’s unicycle at ,, ,and . If it does not exist, explain why. Indicate units of measure.

b)After leaving home, Brian realizes he left his binder at home, and he returns to get it. At what time does he turn around to go back home? Give a reason for your answer.

Suppose Sean starts running from his home to school at t = 0 minutes arriving at school at t = 8. During the time interval, , his velocity, , in miles/minute, is modeled by the velocity function .

c) Who traveled farther Brian or Sean? Show the work that leads to your answer.

d) Who lives further from school, Brian or Sean? Show the work that leads to your answer.

2) Monique drives her car to school, starting at home at minutes and arriving at school at . During the time interval, , her velocity, , in km/minute, is modeled by the piecewise-linear function whose graph is shown below.

a)Find the acceleration, if it exists, of Monique’s car at ,, and . If it does not exist, explain why. Indicate units of measure.

b)What is the total distance Monique traveled in her car?

c)How far is Monique’s home from school?

3) A UPS driver leaves the UPS station at time t = 0 and travels along a straight road. For , the driver’s velocity, in kilometers per minute, is modeled by the piecewise-linear function shown in the graph above.

a) After leaving the UPS station, the UPS driver realizes that he left his driver’s license at the UPS station and returns to get it. At what time does the UPS driver turn around and head back to the UPS station? Give a reason for your answer.

b) Upon arriving at the UPS station, a friend of the UPS driver tosses his driver’s license to him through the side window. At what time does the UPS driver arrive back at the UPS station? Give a reason for your answer.

c) Find the total distance the UPS driver travels during the time interval.

d) At what time is the UPS driver farthest from the UPS station? How far from the UPS station is the UPS driver at that time?

e) At and , find the acceleration of the UPS driver or explain why it does not exist.

f) At , is the UPS driver speeding up, slowing down, or neither. Justify your answer.

g) Write expressions for the UPS driver’s acceleration , velocity , and distance from the UPS that are valid for the time interval .

4) A person starts walking from their home at time t = 0 and travels along a straight road. For , the person’s velocity, in feet per second, is modeled by the piecewise-linear function shown in the graph above.

a) At what times in the interval , if any, does the person change direction? Give a reason for your answer.

b) Find the total distance the person travels during the time interval.

c) At and , find the acceleration of the person or explain why it does not exist.

d) At , is the person speeding up, slowing down, or neither. Justify your answer.

e) Write expressions for the person’s acceleration , velocity , and distance from home that are valid for the time interval .