The problem we are to figure out is this:
To figure out how far the elephant goes before coming to rest we can use calculus to integrate the acceleration finction into a velocity function and further integrate that to come up with a position function.
Though the functions were able to be integrated, which is not always the case, we are now left with an incredibly hard functon to solve. Using calculus we can solve for the time when the velocity of the elephant equals zero. We then plug that time into our position function to come up with x=248.7m
Instead of going through all that trouble we can use excel to set up columns for time at and calculating the acceleration, average acceleration, change of velocity, velocity, average velocity, change in position and distance. We have to choose a very tiny time interval to make sure we do not miss the pont where velocity is closest to zero. We used a time interval of 0.1 seconds.
We then allowed excel to make as many rows as necessary to find the row where our Velocity is closest to zero.
We then followed the same process but simply changed the time interval we used to
0.05sec
0.2sec
1sec
Comparing our numerical results to our analytical results we can see we are right on the mark with our excel process.
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