#3 Non-constant Acceleration problem/Activity

Non-constant Acceleration problem/Activity

introduction:

In the activity, we try to find how far the elephant goes before coming rest.

solve:

Using the Newton's 2nd law F=ma, we can get the acceleration of the elephant.

a(t)=Fnet/m(t)= -8000N / 6500kg-20kg/s*t  =-400/325-t (m/s^2)

Then we can use integrate to find v(t) and x(t). However, the integrate way make the equation be so  complex that we can lots of work, so we are using the Excel to help us calculate.

To find v, we give time interval 0.1(s) to find the average acceleration then we calculate the change in velocity and get the speed at the end of each time interval. v/t=x so that we find the distance.

this is what we do in Excel

between 19.1 to 19.2 v=0

In our chart, we find when time close to 19.7s elephant speed reach 0m/s and travel a little bit more than 248.69804m

conclusions:
1. The result we got from analytically is

19.7s when speed=0 distance =248.7
It means that the analytically and numericallys' answer are the same

2. I try to put time interval= 0.2 and the result is when 19.6 ,v=0.1189  when 19.8, v= -0.1431
that result v range is about +or -0.1 means not quite close to 0 .
Back to time interval 0.1 when t= 19.7 ,v=-0.0121 , means the error is small that we can ignore