Calculus Problem: Solving for t Given x=6.1

[jeremy5561]

Homework Statement

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

Homework 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

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?

 

[SteamKing]

Your acceleration is a function of time. The average acceleration won't give you the correct distance traveled.

 

[haruspex]

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

That formula is only valid for constant acceleration.