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A particle that moves along a straight line has velocity v(t) = t²e-8tm/s after t seconds. This problem involves determining the distance (t) that it will travel during the first t seconds. Step 1. Use integration by parts once with u = t² and du = e-8t dt to begin determining the indefinite integral (antiderivative) of t2e-st. This gives r(t) = ft²e-st dt =+S ¯dt. Step 2. Use integration by parts again to complete finding the indefinite integral (antiderivative) of t²e-8t. This gives z(t) = ft²e-8 dt =+C. Step 3. Use the initial condition (IC) that (0) = 0 to determine the value of the constant C: Step 4. Combine the results of steps 2 and 3 above to determine the distance the particle will travel during the first t seconds: a(t) =

A particle that moves along a straight line has velocity v(t) = t²e-8tm/s after t seconds. This problem involves determining the distance (t) that it will travel during the first t seconds. Step 1. Use integration by parts once with u = t² and du = e-8t dt to begin determining the indefinite integral (antiderivative) of t2e-st. This gives r(t) = ft²e-st dt =+S ¯dt. Step 2. Use integration by parts again to complete finding the indefinite integral (antiderivative) of t²e-8t. This gives z(t) = ft²e-8 dt =+C. Step 3. Use the initial condition (IC) that (0) = 0 to determine the value of the constant C: Step 4. Combine the results of steps 2 and 3 above to determine the distance the particle will travel during the first t seconds: a(t) =

Trigonometry (MindTap Course List)
Trigonometry (MindTap Course List)
10th Edition
ISBN:9781337278461
Author:Ron Larson
Publisher:Ron Larson
Chapter6: Topics In Analytic Geometry
Section: Chapter Questions
Problem 33CT
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A particle that moves along a straight line has velocity v(t) = t²e-8tm/s after t seconds. This problem involves determining the distance (t) that it will travel during the first t seconds. Step 1. Use integration by parts once with u = t² and du = e-8t dt to begin determining the indefinite integral (antiderivative) of t2e-st. This gives r(t) = ft²e-st dt =+S ¯dt. Step 2. Use integration by parts again to complete finding the indefinite integral (antiderivative) of t²e-8t. This gives x(t) = f t²e-8t dt =+C. Step 3. Use the initial condition (IC) that (0) = 0 to determine the value of the constant C: Step 4. Combine the results of steps 2 and 3 above to determine the distance the particle will travel during the first t seconds: a(t) =
Transcribed Image Text:A particle that moves along a straight line has velocity v(t) = t²e-8tm/s after t seconds. This problem involves determining the distance (t) that it will travel during the first t seconds. Step 1. Use integration by parts once with u = t² and du = e-8t dt to begin determining the indefinite integral (antiderivative) of t2e-st. This gives r(t) = ft²e-st dt =+S ¯dt. Step 2. Use integration by parts again to complete finding the indefinite integral (antiderivative) of t²e-8t. This gives x(t) = f t²e-8t dt =+C. Step 3. Use the initial condition (IC) that (0) = 0 to determine the value of the constant C: Step 4. Combine the results of steps 2 and 3 above to determine the distance the particle will travel during the first t seconds: a(t) =
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