Name_______________________________
Period____
Calculus
Review 5.1-5.3, 5.5
1. A particle moves along the x-axis so that its velocity at any time t  0 is given by v(t )  t 2  3 .
(a) If x 1  4 , where is the particle located at t = 4?
(b) What is the average velocity over 0  t  4
2. A particle moves along the x-axis so that its acceleration at any time t  0 is given by a(t )  3t  4 .
(a) If v  0  5 , what is the velocity at t = 6?
(b) What is the average acceleration over 0  t  6
3. A particle traveling along the x-axis is located at x = 5 when t = 0. The motion of the particle, in cm/sec, is
defined by the function v  t   t 2  9 for t  0 .
a. What is the displacement for 0  t  3 ?
b. Where is the particle at time t = 5?
c. Find the average velocity for 0  t  3 ?
d. At what time does the average velocity (from (c)) occur?
4. Find the average velocity of a particle over [0,8] given v(t )  t 2  8t  15.
5. Find the average acceleration of a particle over [0,8] given v(t )  t 2  8t  15.
6. Find the average acceleration of a particle over [0,6] given a(t )  2t 2  4 .
10
7. Describe the meaning of
10
 v(t )dt .
8. Describe the meaning of
0
0
10
10
1
v(t )dt .
9. Describe the meaning of
10 0
11. Describe the meaning of
 a(t )dt .
1
a (t )dt .
10. Describe the meaning of
10 0
x 10   x  0 
.
10  0
12. Describe the meaning of
v 10   v  0 
.
10  0
13. Set up expressions for the following Riemann Sums.
(a) f(x) over [0,12] using 3 midpoint rectangles.
(b) v(t) over [2,20] using 6 left endpoint rectangles
(c) r(p) over [-5,3] using 4 right endpoint rectangles
(d) g(x) over [20,80] using 6 trapezoids
AP Multiple Choice
14.
15.
16.
(A) 2
(B) 4
(C) 6
(D) 36
(E) 42
2015 BC
2012 #1