Complete the free-response questions (FRQs). a) Respond carefully. Follow the directions, and use your notes to help you complete the
assignment. You may wish to review the video instruction associated with this lesson for
reinforcement.
b) Complete each part of the assignment. Be sure to read each question carefully. If you
have any trouble understanding the requirements, ask your teacher for help.
c) Show your work. You may receive partial credit.

FRQ 1
A graphing calculator is required for the following problem.
A particle moves along a straight line. For 0 ≤ t ≤ 5, the position of the particle is given by s(t)=3t+4t^2-t^3.
a) What is the average velocity of the particle over the interval 0 ≤ t ≤ 4?
b) Find a general expression for the velocity of the particle as a function of time, v(t), and determine the value of v at t = 2. Is the particle traveling to the left or the right at this point? Justify your
answer.
c) Find all times t during the interval 0 ≤ t ≤ 5 that the particle changes direction. Justify your answer.
d) At t = 4, is the speed of the particle increasing or decreasing? Justify your answer.

FRQ 2
A graphing calculator may NOT be used for the following problem.
t (minutes) | 0 | 3 | 6 | 10 | 12 | 20 |
v(t)(meters per minute) | 0 | 200 | 500 | 600 | –430 | 360 |
John is riding a bike ride along a straight path. For 0 ≤ t ≤ 0, John’s velocity is given by a differentiable function v. Selected values of v(t), where t is measured in minutes and v(t) is measured in meters per minute, are given in the table above.
a) Use the data table to estimate the value of v’ 8 .
b) Find John’s average acceleration over the interval 6 ≤ t ≤ 1 .
c) Sam is jogging along the same path. For 0 ≤ t ≤ 5, Sam’s velocity is modeled by
0.5t^3-2t^2+100. Find her acceleration at time t = 3.
d) At time t = 3, John is at a position x_J = 200 meters and Sam is at a position x_S = 300 meters, as measured from Sam’s starting point. Find the rate, in meters per minute, at which the distance between John and Sam is changing at time t = 3.