Final answer:
The inverse Laplace transform of 5s/(s−2)² is 5te²⁹t, which corresponds to option B in the given choices.
Step-by-step explanation:
To find the inverse Laplace transform of the function 5s/(s−2)², we need to break it down into a form that we can recognize from the standard Laplace transform tables. Recall that the inverse Laplace transform of s/(s−a)² is te^{at}. This is similar to our given function, except we have an additional multiple of 5 in the numerator.
By comparing our function with the standard form, we can see that a=2, and thus our function is just 5 times the inverse Laplace transform of s/(s−2)². Therefore, the inverse Laplace transform is 5te²⁹t which corresponds to option B. So, the solution is 5te²⁹t.