does not exist, enter DNE.) f(t) = t3 − 9t2 + 24t   e) Draw a diagram to illustrate the motion of the particle and use it to find the total distance (in ft) traveled during the first 6 seconds. f) a. Find the acceleration (in ft/s2) at time t.    b. Find the acceleration (in ft/s2) after 1 second.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.3: The Natural Exponential Function
Problem 56E
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Question
A particle moves according to a law of motion s = f(t), t ≥ 0, where t is measured in seconds and s in feet. (If an answer does not exist, enter DNE.)
f(t) = t3 − 9t2 + 24t
 
e) Draw a diagram to illustrate the motion of the particle and use it to find the total distance (in ft) traveled during the first 6 seconds.
f) a. Find the acceleration (in ft/s2) at time t.
   b. Find the acceleration (in ft/s2) after 1 second.
(g) Graph the position, velocity, and acceleration functions for 0 ≤ t ≤ 6.
Jr
1
2
4
5
30
20
10
-10
30
20
10
-10
S
$
a
a
1 2
4
t
6
5 6
t
30
20
10
-10
V
a
1
2
t
4 5 6
30
O
20
10
-10
V
a
1
2
4
t
5 6
Transcribed Image Text:(g) Graph the position, velocity, and acceleration functions for 0 ≤ t ≤ 6. Jr 1 2 4 5 30 20 10 -10 30 20 10 -10 S $ a a 1 2 4 t 6 5 6 t 30 20 10 -10 V a 1 2 t 4 5 6 30 O 20 10 -10 V a 1 2 4 t 5 6
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