Maths... err... physics... err... ouch!

Ok... so I was monkeying with some basic physics... and hurt myself.

Given the formula a = (v^2 - u^2) / 2s where u is initial velocity, v is final velocity, s is distance and a is acceleration... then given the following:
u = 0
v = 211 fps
s = 4060 feet
a = 44511 / 8120
a = 5.48 fps^2
Given that f = m*a where m is mass, a is acceleration and f is force...
m = 20200 pounds
a = 5.48 fps^2
f = 20200 * 5.48
f = 110729 pounds
How does an aircraft with a maximum of 8200 pounds of total engine thrust actually accomplish those figures? The figures I used are from takeoff charts for an aircraft. My mind is obviously missing something. Anyone want to show me what/where?
That page has the second equation on it... f = m*a because mass and acceleration are constants... which for this discussion is accurate.

Slowly, slowly, catchee speeds up monkey.

> 38 secs worth of t, (guesstimation @ zero drag)

v = Vr
a = averaged acceleration fps (to reach Vr)
f = pounds thrust expended to achieve that rate of acceleration (@ zero drag)

Apologies if above is total b*ll*cks.
Right right right. 1 lb thrust is 1 lb force against gravity (9.8 m/s^2 or 32.15 ft/s^2)

110729/32 => 3444
Ok, so the only thing I see different is units. Is the result of the calculations when using pounds and fps^2 not a valid unit?

And Ron's post finished the thought for me... thanks everyone!
You had the units right until you compared to the 8200 lb thrust engine => 8200 * 32.17 = 263794 lbs
What can I say... it's rocket science... and I'm not. LOL Thanks for helping me straighten it out everyone.