1. By: Hawa Soumare

2.  Question

3.   Part A: Finding zeros  Part B: Integration  Part C: Interpreting graphs  Part D: Finding derivative and comparison Plan

4.   First, set |V(t)| = 2. Which you then change to |V(t)| - 2 = 0. You plug this into the calculator, graph it, and find the zeros between the interval 2 ≤ t ≤ 4 Part A: Find all values of t in the interval 2 ≤ t ≤ 4 for which the speed of the particle is 2.

5.   We can find s(5) by plugging in 5 for t  Remember it is given that s(0) = 10 Part B: Write an expression involving an integral that gives the position s ( t ). Use this expression to find the position of the particle at time t = 5.

6.   The particle will change direction when v(t) changes signs. You graph v(t) between 0 ≤ t ≤ 5 and see where it passes the x-axis. This occurs at t = 0.536 and t =3.318. v ( t ) changes sign from negative to positive at time t = 0.536033. v ( t ) changes sign from positive to negative at time t = 3.317756.  Therefore, the particle changes direction at time t = 0.536 and time t = 3.318 (or 3.317). Part C: Find all times t in the interval 0 ≤ t ≤ 5 at which the particle changes direction. Justify your answer.

7.   Speed is increasing when the signs of v(t) and a(t) are the same and decreasing when the signs are different  Using the calculator you will find: Part D: Is the speed of the particle increasing or decreasing at time t = 4 ? Give a reason for your answer.

8.   http://askmrcalculus.com/2013_AB_2.gif http://askmrcalculus.com/2013_AB_2.gif  http://media.collegeboard.com/digitalServices/pdf /ap/apcentral/ap13_calc_ab_scoring_guidelines.pdf http://media.collegeboard.com/digitalServices/pdf /ap/apcentral/ap13_calc_ab_scoring_guidelines.pdf  http://socratic.org/questions/how-do-you-solve- the-ap-calculus-ab-2013-free-response-question-2- http-media-col http://socratic.org/questions/how-do-you-solve- the-ap-calculus-ab-2013-free-response-question-2- http-media-col Citations