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AP CALCULUS STUDENT HANDOUT Understanding the Vocabulary of Motion and Definite Integrals Part 1 Use the words and phrases in the word bank to complete the fill-in-the-blank sentences given. Note: Each word or phrase will be used only once. Word Bank absolute value position starting position displacement speed velocity 1. To find the new position of a particle moving on the x-axis, add to the integral of from starting time to new time. 2. To find total distance travelled, integrate , which is the of velocity. 3. To find the change in _position integrate velocity over the time interval. This is also called displacement Part 2 A particle moves along the x-axis so that at time t its position is given by x(t) and 2 velocity given by v(t) . At t = 2, the particle is located at x = 5. The following graph gives the velocity of the particle over the 2 3 4 51 6 time interval from t = 2 to t = 7. Match the numerical expressions to their verbal statements. -2 A. 3+2 B. 3-2 Q . 5 + 3 - 2 1. Total distance travelled by the particle over the interval from t = 2 to t = 7 C 2. Position of the particle at t = 7 3. Change in position between t = 2 and t = 7 CollegeBoard