AP calculus AB

1. AP calculus AB Angela Qu AP calculus AB 11th grade Pd. 2-3

2. 2003 AP calculus AB Free Response Question [Calculator problem!]

3. a) Find the acceleration of the particle at time t=2. Is the speed of the particle increasing at time t=2? Why or why not? Because the velocity of the particle and the acceleration of the particle at time t=2 has different signs, V(t)<0 a(t)>0 So the speed of the particle is decreasing at time t=2 If the velocity and the acceleration has the same sign, the particle is increasing; if not, the particle is decreasing.

4. b) Find all times t in the open interval 0<t<3 when the particle changes direction. Justify your answer. Because the particle changes direction, so rate of change of the displacement V(t)=0 2.507 Because 0<t<3 So t≠-1 So t=2.507 Eliminate

5. c) Find the total distance traveled by the particle from time t=0 until time t=3. “Distance” indicates absolute value, area under the curve

6. d) During the time interval 0<t<3, what is the greatest distance between the particle and the origin? Show the work that leads to your answer. The greatest distance between the particle and the origin will occur where the function f(x) achieves a relative max or a relative minimum. 2.507

7. Citation: www.collegeboard.com

8. THANK YOU.