A brick falls from the top of a building and strikes the ground with a velocity of 19.6m/s. How long does the brick fall?

Are you asking how long as in time or how long as in distance? Since Velosity = displacement/time elapsed does the problem give more information than the velocity? If so you could say time = V/displacement and Displacement = V* time

... acceleration due to gravity 9.81 meters per second squared... Its been ten years since high school but that is it no?

Based on the number given in the question, I'd assume acceleration due to gravity is 9.8m/s^2.

The equation for velocity in terms of constant acceleration is:

v(t) = v0 + a*t

Where v0 is the initial velocity, a is the acceleration, and t is the time. You can now solve for time given v(t) = 19.6, v0 = 0, and a = 9.8.

If the question is asking "how long" in terms of total distance fallen (which I don't think it is), start by solving for the time, then use the formula

d = v0*t + a*t^2/2, which you get by integrating v(t) = v0 + a*t.

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I would go about solving this problem in the following manner...

acceleration = (final velocity - initial velocity) / time

Our acceleration in this problem is the acceleration due to gravity which is 9.8 m/s/s

Our final velocity is 19.6 m/s/s as indicated by the problem.

Our initial velocity is 0 m/s/s which is derived from the fact that before it began to fall off the building, it was not moving.

We can then solve for time.

9.8 = (19.6 - 0) / t

9.8 = 19.6/t

multiply both sides by t

9.8t = 19.6

divide both sides by 9.8

t = 2

The brick fell for 2 seconds.

I hope that this was helpful.