Non-Constant acceleration problem/activity

Before this lab, we usually did some problem about constant acceleration, but, now, we were going to handle those problem on non-constant acceleration, and use program in computer to solve other same style problem.
Here is the question:
A 5000-kg elephant on friction less roller skates is going 25 m/s when it gets to the bottom of a
hill and arrives on level ground. At that point a rocket mounted on the elephant’s back generates a constant 8000 N thrust opposite the elephant’s direction of motion.The mass of the rocket changes with time (due to burning the fuel at a rate of 20 kg/s) so that the m(t) = 1500 kg – 20 kg/s·t.
Find how fat the elephant goes before coming to rest.

For solve this question, in the first step, we need to find the equation about the acceleration of the elephant + rocket system with Newton's second law:

Second step, we can integrate the acceleration from 0 to t find the instant velocity and then derive the equation for v(t):

and we get:

Third step, we continued to integrate the velocity from 0 to t to find changed position and then derive the equation for x(t):

Therefore we can get:

And then solve v(t) to find the time at which v=0.After we got the time, and we can lug it into the expression for x(t) to find how far that elephant goes, and we got: 249m.

After we solved the problem, we can use Excel to solve other same style problem.

We created a row of time which incremented by 0.1 seconds for at least 220 rows. We would calculate the acceleration at any time in column B, and input the formula into cell B3. In column C, we calculated the average acceleration. In column D, we calculated the change in velocity. In column F, we calculated the speed.

Conclusion:

1. They are almost same between two results from doing problem analytically and doing it numerically.

2. The way you wanted to know whether the time interval is close enough to get a good result you could try to change the interval of seconds on the first table and watch how much the distance was changes. If we did it several times and noticed the answer did not change, we could assume the time interval is well.