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The displacement (in meters) of a particle moving in a straight line is given by s = t - 9t + 19, where t is measured in seconds. (a) Find the average velocity over each time interval. (i) [3, 4] m/s (ii) [3.5, 4] m/s (iii) [4, 5] m/s (iv) [4, 4.5] m/s

The displacement (in meters) of a particle moving in a straight line is given by s = t - 9t + 19, where t is measured in seconds. (a) Find the average velocity over each time interval. (i) [3, 4] m/s (ii) [3.5, 4] m/s (iii) [4, 5] m/s (iv) [4, 4.5] m/s

Calculus: Early Transcendentals
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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The displacement (in meters) of a particle moving in a straight line is given by s = t2 - 9t + 19, where t is measured in seconds. (a) Find the average velocity over each time interval. (i) [3, 4] m/s (ii) [3.5, 4] m/s (iii) [4, 5] m/s (iv) [4, 4.5] m/s (b) Find the instantaneous velocity when t = 4. m/s
Transcribed Image Text:The displacement (in meters) of a particle moving in a straight line is given by s = t2 - 9t + 19, where t is measured in seconds. (a) Find the average velocity over each time interval. (i) [3, 4] m/s (ii) [3.5, 4] m/s (iii) [4, 5] m/s (iv) [4, 4.5] m/s (b) Find the instantaneous velocity when t = 4. m/s
Expert Solution
Step 1

Given:

s=t2-9t+19

For (a),

(i) [3, 4]

Average velocity = s(4)-s(3)4-3=-1-11=-2.

(ii) [3.5, 4]

Average velocity = s(4)-s(3.5)4-3.5=-1+0.250.5=-1.5.

(iii) [4, 5]

Average velocity = s(5)-s(4)5-4=-1+11=0.

(iv) [4, 4.5]

Average velocity = s(4.5)-s(4)4.5-4=-1.25+10.5=-0.5.

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