3-Sep.-2014: Non-Constant Acceleration Problem/Activity

This activity was completed in class.

PURPOSE: To learn how to solve problems with a non-constant acceleration.



A 5000-kg elephant on frictionless 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.



To find how far the elephant goes before coming to rest, we were provided with multiple methods.

1. Newton's 2nd law gives us the acceleration of the elephant and rocket system as a function of
2. Integrating the acceleration from 0 to t to find Δv and then deriving an equation for v(t):
   
    
3. Integrating the velocity from 0 to t to find Δx and then deriving an equation for x(t):

Another method would be, solving v(t) to find the time at which v = 0 and then, using that time to plug into the exprestion for x(t) to find how far the elephant goes. 

We used a spreadsheet to find values in the problem. We set things up so that the time increments by 0.1 seconds and continues to about the 220th row on the sheet.

To calculate the acceleration in the sheet, we used the formula for a(t) and filled down.

We also calculated the average acceleration for the first 0.1 s interval

We then calculated the change in velocity from interval to interval.

We first let the spreadsheet calculate the values with time intervals of 1sec., then 0.1s, then 0.05s.

We found that the elephant reaches a distance of about 248.7m.