3/2 Non-constant Acceleration Problem/Activity Solution

Purpose: To prove that non-constant acceleration problems can be done numerically besides just analytically. 

Procedure:In the first part of the lab we were given a problem (FIGURE (1)) that turned out to be very difficult to integrate.

FIGURE (1)

Luckily, we are able to use Excel to solve the problem numerically. We created a spreadsheet (FIGURE (2)) and set up a time interval, instantaneous acceleration, average acceleration, ∆velocity, instantaneous velocity, and distance. 

FIGURE (2)

To set up the spreadsheet, we started with acceleration because virutually all the other equations we need will need acceleration. In order to calculate the acceleration at each time interval we used the equation: 

a= 2t²

For average acceleration we used the equation:

 

For ∆velocity we used the equation: 

∆v= 

For instantaneous velocity:

v=v₀+∆v

And for distance: 

x= 

After entering all these equations in excel, we can evaluate any of the variables we have at any time interval, acceleration, velocity, etc.. 

Conclusion:

In the problem, we are trying to find distance before coming to rest. So our velocity should be zero. In the analytically found result, this gives us a time of 19.69 seconds, and if we plug that into our expression for x, then we will get 248.7 meters.
As shown in FIGURE (2), at 19.6 seconds, our distance is 248.7 meters. We can also tell that 19.6 seconds is the correct time to choose because our velocity is very near zero (the closest on our spreadsheet). These results prove that our spreadsheet works!