Non-constant acceleration problem/ Activity

Non-constant acceleration problem/ Activity

Purpose: Use Excel to solve the non-constant acceleration problem numerically and compare the result to the one done by analytic way.

Activity:
Analytic integration:
1. Set up a function for acceleration based on the problem.

2. integrate the acceleration from 0 to t to find delta v and then derive an equation for v(t).

3.integrate the velocity from 0 to t to find delta x and then derive an equation for x(t).

4.solve v(t) to find the time at which v=0.

5.use the time derived in 4 and plug that into expression for x(t) to find how far the elephant goes.

Numerical integration:

1.set up the column of t, a, a_avg, delta v, v, delta x, and x with A2=0, E2=25, G2=0.

2.Input the formula =A2+0.1 into cell A3.

3.Input the formula =-400/(325-A2) into cell B2.

4.Input the formula =(B3+B2)/(A3-A2) into cell C3.

5.Input the formula =C3*(A3-A2) into cell D3.

6.Input the formula =25+D3 into cell E3.

7.Input the formula =

8.Input the formula =G2+F3 into cell G3.

9.Fill down the contents of Row 3 to the rest of the spreadsheet and determine when and where the elephant comes to rest. 

The distance is close to 248.69.
10.Change the time interval to 0.05s instead of 0.1s and see if it makes a difference.

The distance is close to 248.69.
11.Change the time interval to 1s instead of 0.1s and see if it makes a difference.

The distance is close to 248.67.

Conclusion:
1.Both analytic and numerical integration give us the similar result.
2.In the numerical integration, the smaller time interval, the more accurate result we will get.