Final answer:
To calculate the Laplace transform of the function 5u(t - 2), we sketch the time function, recognize the effects of the unit step function, and utilize the table of Laplace transforms to find that the transform is 5e^{-2s}/s.
Step-by-step explanation:
The question involves calculating the Laplace transform of a given time function 5u(t - 2), where u(t - 2) is the unit step function that shifts to the right by 2 units on the time axis. To sketch this function, we plot a graph that is zero for t < 2 and becomes 5 for t ≥ 2. After sketching, we use the definition of the Laplace transform to transform the time function into the s-domain.
The Laplace transform of 5u(t - 2) is given by:
Recognize that the step function shift results in the multiplication of the function by e^{-2s} in the s-domain.
Identify the Laplace transform of the unit step function u(t) from the table which is \frac{1}{s}.
Account for the scaling factor of 5 and the shift of 2 to find the Laplace transform L{5u(t - 2)} = 5e^{-2s}/s.