This should probably go in the physics help forum website, but phf seems to have a few glitches that have made it difficult for me to post there.
Anyways, it's really just a simple algebra question that has probably been asked thousands of times:
In Newton's distance formula for a constantly accelerating object, to wit:
why don't the t's cancel??
I.e. why isn't Newton's formula instead:
which simply says that the distance travelled is equal to the average of the initial and final velocities multiplied by the time taken. Which, for constant acceleration, is correct.
(Geometrically, the distance travelled = area under the v-t graph. For constant acceleration this is a straight line graph, and the formula is simply the area of a trapezium.)