John in Kansas says: " But Lyle:

(feet/second)/second, evaluated, is ft/(second^2) and it is a simple "seconds squared" for any algebraic evaluation.

Common elementary mistake, John. Look at brucie's excellent example. If evaluated as brucie has properly done, the results are:
after 1sec velocity is 32ft/sec
after 2 sec velocity is 64ft/sec
after 3 sec velocity is 96ft/sec
after 4 sec velocity is 128ft'sec

If calculated by squareing the seconds, the results are:
after 1 sec velocity is 32*1^2 = 32ft/sec
after 2 sec velocity is 32*2^2 = 128ft/sec
after 3 sec velocity is 32*3^2 = 288ft/sec
after 4 sec velocity is 32*4^2 = 512ft/sec


And a big THANK YOU to CarolC - don't often get a "line" like that!