Feet per second is a unit of velocity, but not necessarily the same thing. Velocity could be in meters per hour or feet per second could be a measure of speed, which does not take direction into account, as velocity does.
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Initial velocity can be measured in the same units as any other velocity. In SI, that would be meters per second, but often km / hour are used, or (in a minority of countries) feet/second or miles/hour.
The units are the same (metres per second) except that the velocity also has the direction of motion associated with it.
After one second the rock will be traveling at 9.8m/s (meters per second) or 32.17 feet per second. The height of the building is irrevelant, because gravity always pulls with the same force of 9.8m/s2 (meters per second squared), which means that every second the velocity will increase by 9.8m/s. This is why after one second the rock will be going 9.8m/s.
Linear feet and feet means the same thing.
The result will also be a velocity vector. Draw the first vector. From its tip draw the negative of the second vector ( ie a vector with the same magnitude but opposite direction). The the resultant would be the vector with the same starting point as the first vector and the same endpoint as the second. If the two vectors are equal but opposite, you end up with the null velocity vector.