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Video Example 4 A particle moves in a straight line and has acceleration given by a(t) = 18t + 8. Its initial velocity is v(0) = -6 cm/s, and its initial displacement is s(0) = 9 cm. Find its position function, s(t). Solution Since v'(t)= a(t) = 18t + 8, antidifferentiation gives the following. v(t) = 8t + C = Note that ✓(0) = C. But we are given that v(0) = -6, so C = [ Since v(t) = s'(t), s is the antiderivative of v. s(t) = +D - 6t + D This gives s(0) = D. We are given that s(0) = 9, so D = and v(t) = and the required position function is s(t) =

Video Example 4 A particle moves in a straight line and has acceleration given by a(t) = 18t + 8. Its initial velocity is v(0) = -6 cm/s, and its initial displacement is s(0) = 9 cm. Find its position function, s(t). Solution Since v'(t)= a(t) = 18t + 8, antidifferentiation gives the following. v(t) = 8t + C = Note that ✓(0) = C. But we are given that v(0) = -6, so C = [ Since v(t) = s'(t), s is the antiderivative of v. s(t) = +D - 6t + D This gives s(0) = D. We are given that s(0) = 9, so D = and v(t) = and the required position function is s(t) =

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section: Chapter Questions
Problem 18T
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Question
A particle moves in a straight line and has acceleration given by 
a(t) = 18t + 8.
 Its initial velocity is 
v(0) = −6 cm/s,
 and its initial displacement is 
s(0) = 9 cm.
 Find its position function, 
s(t).
 
Example 6 Video A particle moves in a straight line and has acceleration given by a(t) = 18t + 8. Its initial velocity is v(0) = -6 cm/s, and its initial displacement is s(0) = 9 cm. Find its position function, s(t). Solution Example 4 Since v'(t) = a(t) = 18t + 8, antidifferentiation gives the following. v(e) = ([ + 8t + C = Note that v(0) = C. But we are given that v(0) = -6, so C = and v(t) = Since v(t) = s'(t), s is the antiderivative of v. s(t) = 9 +D +C - 6t+ D This gives s(0) = D. We are given that s(0) = 9, so D= [ and the required position function is s(t) =
Transcribed Image Text:Example 6 Video A particle moves in a straight line and has acceleration given by a(t) = 18t + 8. Its initial velocity is v(0) = -6 cm/s, and its initial displacement is s(0) = 9 cm. Find its position function, s(t). Solution Example 4 Since v'(t) = a(t) = 18t + 8, antidifferentiation gives the following. v(e) = ([ + 8t + C = Note that v(0) = C. But we are given that v(0) = -6, so C = and v(t) = Since v(t) = s'(t), s is the antiderivative of v. s(t) = 9 +D +C - 6t+ D This gives s(0) = D. We are given that s(0) = 9, so D= [ and the required position function is s(t) =
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