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Question : A freight train travels at v = 60(1 - e^-t) ft/s, where t is...

A freight train travels at v = 60(1 - { e }^{ -t }) ft/s, where t is the elapsed time in seconds. Determine the distance traveled in three seconds, and the acceleration at this time.

Question Data is a breakdown of the data given in the question above.
  • Freight train velocity: v = 60(1 – e^(-t)) ft/s
  • Elapsed time: t = 3 seconds
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Step 1:
We are given the equation for velocity as v = 60(1 - e^...
Step 2:
To find the displacement (s), we need to integrate the ...
Step 3:
Integrating the velocity function, we get s = 60(t + e^...
Step 4:
Evaluating the integral at t = 3, we find s = 123 ft. T...
Step 5:
To find the acceleration (a), we take the derivative of...
Step 6:
At t = 3s, we can evaluate the acceleration function to...
In summary, the object's displacement after 3 seconds i...