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Calculus Problem

  1. Oct 14, 2013 #1
    1. The problem statement, all variables and given/known data
    Well I've pretty much boiled the problem down to this:

    Let a = 1.767+0.3213t
    v(0)=0
    x(0)=0

    then I got
    x(t)=(0.8835+0.05355 t) t^2

    Given x=6.1

    Solving for t I got t=2.45175

    But i'm just curious. If I calculate average acceleration I get a_av=2.16.

    If I now apply x=1/2at^2 using a average I don't get 6.1

    2. Relevant equations
    Using calculus I turned a=1.767+0.3213t to
    x=(0.8835+0.05355 t) t^2

    Given x is 6.1 I solve t=2.45175


    3. The attempt at a solution

    But now when I use the average velocity trick and then use x= 1/2at^2 I don't get 6.1. Is my solution incorrect?
     
  2. jcsd
  3. Oct 15, 2013 #2

    SteamKing

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    Your acceleration is a function of time. The average acceleration won't give you the correct distance traveled.
     
  4. Oct 15, 2013 #3

    haruspex

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    That formula is only valid for constant acceleration.
     
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