AP Calculus AB Unit 6: Applications of the Definite Integral - Lesson 4 Practice Problems: 1. A bug is walking along the x-axis and its velocity, in meters per second, is given by the equation v(t) = 5.6cos (2t). Ifx (1) -4, find the following: = a. What is the position of the bug when t = 7? √(t) = 5.6 Cos(2 €) b. What is the total distance the bug traveled over the interval 1 ≤ t≤ 5 seconds? Siv(e)l de $13 c. Find a(3). Is the bug speeding up or slowing down at t = 3 seconds. Explain your reasoning. a (t) = 5.6C03 (24).2 =-11.2 Sin (22) 13 35 3-0 ²5. a (3) = -11.2 Sin (2(3)) The bug is speeding up because -11.2 Sin (6) and a(t) are both + d. Find the average velocity of the bug over the interval 0 ≤ t ≤ 3 seconds. v(t) dx 2 = 3.1294 m/s v (8) = 5.6 cos (2(3) = 5.3769 3) 5.6 cos (26) dt = -0.2607 or -0.261 2.1 2. The velocity (in feet per second) of a particle moving along a line is v(t) = t³ - 10t² + 29t-20, where t is the time in seconds. a. What is the displacement of the particle on the time interval 1 ≤t ≤5? th 10t3 3 55 "SVEIde = ³f 14 - 102²0 + 20€² 4 2 10 (13 3 3 - 2 - 29 (3) ² - 20(3)) -(4-10 (1) 29 (1) ²4 2₂0(1)) 3 b. What is the total distance travelled by the particle on the time interval 1 ≤t ≤5? - 20t 20€ 3333
AP Calculus AB Unit 6: Applications of the Definite Integral - Lesson 4 Practice Problems: 1. A bug is walking along the x-axis and its velocity, in meters per second, is given by the equation v(t) = 5.6cos (2t). Ifx (1) -4, find the following: = a. What is the position of the bug when t = 7? √(t) = 5.6 Cos(2 €) b. What is the total distance the bug traveled over the interval 1 ≤ t≤ 5 seconds? Siv(e)l de $13 c. Find a(3). Is the bug speeding up or slowing down at t = 3 seconds. Explain your reasoning. a (t) = 5.6C03 (24).2 =-11.2 Sin (22) 13 35 3-0 ²5. a (3) = -11.2 Sin (2(3)) The bug is speeding up because -11.2 Sin (6) and a(t) are both + d. Find the average velocity of the bug over the interval 0 ≤ t ≤ 3 seconds. v(t) dx 2 = 3.1294 m/s v (8) = 5.6 cos (2(3) = 5.3769 3) 5.6 cos (26) dt = -0.2607 or -0.261 2.1 2. The velocity (in feet per second) of a particle moving along a line is v(t) = t³ - 10t² + 29t-20, where t is the time in seconds. a. What is the displacement of the particle on the time interval 1 ≤t ≤5? th 10t3 3 55 "SVEIde = ³f 14 - 102²0 + 20€² 4 2 10 (13 3 3 - 2 - 29 (3) ² - 20(3)) -(4-10 (1) 29 (1) ²4 2₂0(1)) 3 b. What is the total distance travelled by the particle on the time interval 1 ≤t ≤5? - 20t 20€ 3333
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Question
A bug is walking along the
Transcribed Image Text:AP Calculus AB
Unit 6: Applications of the Definite Integral - Lesson 4
Practice Problems:
1. A bug is walking along the x-axis and its velocity, in meters per second, is given by the equation v(t) =
5.6cos (2t). Ifx (1) -4, find the following:
=
a. What is the position of the bug when t = 7?
√(t) = 5.6 Cos(2 €)
b. What is the total distance the bug traveled over the interval 1 ≤ t≤ 5 seconds?
Siv(e)l de $13
c. Find a(3). Is the bug speeding up or slowing down at t = 3 seconds. Explain your reasoning.
a (t) = 5.6C03 (24).2
=-11.2 Sin (22)
13
35
3-0 ²5.
a (3) = -11.2 Sin (2(3)) The bug is speeding up because
-11.2 Sin (6)
and a(t) are both +
d. Find the average velocity of the bug over the interval 0 ≤ t ≤ 3 seconds.
v(t) dx
2
= 3.1294 m/s v (8) = 5.6 cos (2(3)
= 5.3769
3) 5.6 cos (26) dt = -0.2607 or -0.261
2.1
2. The velocity (in feet per second) of a particle moving along a line is v(t) = t³ - 10t² + 29t-20, where t is the
time in seconds.
a. What is the displacement of the particle on the time interval 1 ≤t ≤5?
th
10t3
3
55
"SVEIde = ³f 14 - 102²0 + 20€²
4
2
10 (13
3
3
-
2
-
29 (3) ² - 20(3)) -(4-10 (1) 29 (1) ²4 2₂0(1))
3
b. What is the total distance travelled by the particle on the time interval 1 ≤t ≤5?
- 20t
20€
3333
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