AP Calculus AB Individual Project

1. AP Calculus AB Individual Project Acceleration And ApproximationBy Sherman Tung

2. AP Calculus AB 1998 FRQ Problem 3 The graph of the velocity v(t), in , of a car traveling on a straight road, for 0 ≤ t ≤ 50, is shown above. A table of values for v(t), at 5 second intervals of time t, is shown to the right of the graph.

3. (A) During what intervals of time is the acceleration of the car positive? Give a reason for your answer Acceleration is positive on (0,35) and (45,50). Velocity is increasing in both intervals

4. (B) Find the average acceleration of the car, in , over the interval. Mean Value Theorem: or 1.44 ft/sec^2

5. (C) Find one approximation for the acceleration of the car, in , at t = 40. Show the computations you used to arrive at your answer. Determine the Slope of the Tangent Line Mean Value Theorem: Using the points (35,90) and (40,75) = The approximation at t = 40 using points (35,90) and (40,75) is

6. (D) Approximate with a Riemann sum, using the midpoints of five subintervals of equal length. Using correct units, explain the meaning of this integral. Example Midpoint Riemann sum:

7. (D) Approximate with a Riemann sum, using the midpoints of five subintervals of equal length. Using correct units, explain the meaning of this integral.

8. AP Calculus AB 1998 FRQ Problem 3 Complete! The End to Calculations

9. Citations • http://apcentral.collegeboard.com/apc/members/repository/sg_calcab_98_9669.pdf • http://en.wikipedia.org/wiki/Riemann_sum • Paint