Answer
$\frac{2e^{-5s}}{s^2}$
Work Step by Step
Given: $f(t)=2(t-5)u_5(t)$
Using the Convolution Theorem
$L[f(s)]=L[2(t-5)u_5(t)]\\
=e^{-5s}L[F(t)]$
With $F(T)=2T$
we have:
$L[f(s)]=e^{-5s}L[2t]\\
=\frac{2e^{-5s}}{s^2}$
Differential Equations and Linear Algebra (4th Edition)
by Goode, Stephen W.; Annin, Scott A.
Published by
Pearson
ISBN 10:
0-32196-467-5
ISBN 13:
978-0-32196-467-0
Chapter 10 - The Laplace Transform and Some Elementary Applications - 10.10 Chapter Review - Additional Problems - Page 718: 16
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