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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Help with finding distance if it's not 109-(-3)
![Let \( s(t) = t^3 - 6t^2 + 9t - 3 \) for \( 0 \leq t \leq 7 \) denote the position of an object moving along a line. Find:
- The velocity at time \( t \) is \( 3t^2 - 12t + 9 \).
- The acceleration at time \( t \) is \( 6t - 12 \).
- Find the initial position \( -3 \) and the ending position \( 109 \).
- Find the total distance traveled by the object \( 112 \).
- Find where the velocity is positive \( [0,1) \cup (3,7] \). Use interval notation.
- Find where the acceleration is positive \( (2,7] \). Use interval notation.
If the answer includes more than one interval, write the intervals separated by the "union" symbol, \( \cup \). If needed, enter \(\infty\) as INF and \(-\infty\) as -INF.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7efc92fb-f6e6-45fd-bcd8-2c3c0a4ba455%2F7b8e918c-add6-42bd-91b0-ed33c69df920%2F8h5fgpr_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Let \( s(t) = t^3 - 6t^2 + 9t - 3 \) for \( 0 \leq t \leq 7 \) denote the position of an object moving along a line. Find:
- The velocity at time \( t \) is \( 3t^2 - 12t + 9 \).
- The acceleration at time \( t \) is \( 6t - 12 \).
- Find the initial position \( -3 \) and the ending position \( 109 \).
- Find the total distance traveled by the object \( 112 \).
- Find where the velocity is positive \( [0,1) \cup (3,7] \). Use interval notation.
- Find where the acceleration is positive \( (2,7] \). Use interval notation.
If the answer includes more than one interval, write the intervals separated by the "union" symbol, \( \cup \). If needed, enter \(\infty\) as INF and \(-\infty\) as -INF.
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