A dragster launching down the quarter mile covers distance according to one of motion's greatest hits: displacement equals initial velocity times time, plus one-half times acceleration times time squared. In symbols: s = ut + ½at². The first term is the coasting distance — how far you would roll at your starting speed — and the second is the bonus distance the acceleration piles on.

Watch a jet take off and you see both terms working. The plane rolls at increasing speed down the runway, and the ½at² term dominates because the engines pour on constant thrust. Accident investigators run the same formula backward: from skid-mark length and estimated deceleration, they recover how fast a car was moving when the brakes locked.

This calculator evaluates the full equation from three inputs. Type the starting velocity in the Initial Velocity (u) box, the elapsed time in the Time (t) box, and the steady acceleration in the Acceleration (a) box — feet per second and seconds keep the answer in feet. The Displacement (s) box reports how far the object traveled. A car accelerating from rest at 15 ft/s² for 10 seconds covers 750 feet — most of a quarter mile before the second term finishes its work.

With the pre-filled defaults — Initial Velocity (u) 0, Time (t) 5, Acceleration (a) 2 — the Displacement Calculator returns Displacement (s) 25.0000. Change any input and those results update instantly, so you can see exactly how each number you enter moves the answer.