A particle moves according to a law of motion s = f(t), t 2 0, where t is measured in seconds and s in feet. (t) = te t/5 (a) Find the velocity at time t (in ft/s). v(t) = (t – 5)e 5 (b) What is the velocity after 2 s? (Round your answer to two decimal places.) v(2) = [0.40 ft/s (c) When is the particle at rest? t = [0 (d) When is the particle moving in the positive direction? (Enter your answer using interval notation.) [0,5) (e) Find the total distance traveled during the first 12 s. (Round your answer to two decimal places.) 1.09 X ft
A particle moves according to a law of motion s = f(t), t 2 0, where t is measured in seconds and s in feet. (t) = te t/5 (a) Find the velocity at time t (in ft/s). v(t) = (t – 5)e 5 (b) What is the velocity after 2 s? (Round your answer to two decimal places.) v(2) = [0.40 ft/s (c) When is the particle at rest? t = [0 (d) When is the particle moving in the positive direction? (Enter your answer using interval notation.) [0,5) (e) Find the total distance traveled during the first 12 s. (Round your answer to two decimal places.) 1.09 X ft
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section: Chapter Questions
Problem 18T
Related questions
Concept explainers
Equations and Inequations
Equations and inequalities describe the relationship between two mathematical expressions.
Linear Functions
A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.
Question
How do I solve C, E, and H?
Transcribed Image Text:A particle moves according to a law of motion s = f(t), t 2 0, where t is measured in seconds and s in feet.
f(t) = tet/5
(a) Find the velocity at time t (in ft/s).
v(t) =
(† – 5)e
(b) What is the velocity after 2 s? (Round your answer to two decimal places.)
v(2) = [0.40
v ft/s
(c) When is the particle at rest?
t = [0
X S
(d) When is the particle moving in the positive direction? (Enter your answer using interval notation.)
[0,5)
(e) Find the total distance traveled during the first 12 s. (Round your answer to two decimal places.)
1.09
X ft
(f) Find the acceleration at time t (in ft/s?).
(1 – 10)e (¿)
25
a(t) =
Find the acceleration after 2 s. (Round your answer to three decimal places.)
a(2) = (-0.215
v ft/s?
(g) Graph the position, velocity, and acceleration functions for the first 12 s.
y
y
2.0
2.0
1.5
1.5
1.0
1.0
0.5
0.5
6.
8
10
12
6.
8.
10
12
-0.5
-0.5
- 1.0F
o-1.0F
y
y
2.0
2.0
1.5
a
1.5
1.0
1.0
0.5
0.5
8.
10
12
10
12
-0.5
-0.5
о-1.0
o-1.0F
(h) When, for 0st< o, is the particle speeding up? (Enter your answer using interval notation.)
(6,00)
When, for 0 st < ∞, is it slowing down? (Enter your answer using interval notation.)
[0,6)
Expert Solution
Step 1
Given-
s= f(t) = te^(-t/5)
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 1 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781337278461
Author:
Ron Larson
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781337278461
Author:
Ron Larson
Publisher:
Cengage Learning