Lab#3 Non-constant acceleration problem/Activity solution

Numerical integration:

 1. Open up a new Excel spreadsheet and enter the following:
     A1: △t=
     B1: 0.2
     A2: t
     B2: a
     C2: a_avg
     D2: △v
     E2: v
     F2: V_avg
     G2: △x
     H2: x
 2. Fill down to cell A3
 3. Input a=2t^2 into cell B3 that will let you calculate the acceleration at any time.
 4.Fill that formula down to cell B4.
 5. in cell C4 calculate the average acceleration for that first 2.0 s interval.a_avg=(a0+a1)/2
 6. in cell D4 calculate the change in velocity for that first time interval. △v=a_avg*△t
 7. in cell E4 calculate the speed at the end of  that time interval. v=v0+△v
 8. in cell F4 calculate the average speed of the elephant. △v=(v0+v1)/2
 9. in cell G4 calculate the change in position. △x=v_avg*△t
 10. in cell H4 calculate the position of the elephant. x=x0+△x
 11. "Fill Down" the contents of Row 4 to the rest of the spreadsheet.

Activity solution:

    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 -a0 kg/s*t.
  Find how far the elephant goes before coming to rest.