Displacement from Final Velocity (d = vt − ½at²)

This is the one of the five kinematic equations that most courses list last and most students forget: it is the twin of d = v₀t + ½at², written from the far end of the motion instead of the near end. Use it when the final velocity is known and the starting speed is what you are missing: a car's speed as it crosses a line, a ball's speed as it lands. The minus sign is not a special case; it falls straight out of substituting v₀ = v − at into the more familiar form, and it is why the answer is smaller than vt whenever the object was speeding up.

Solving it for time takes care. Rearranged for t it becomes a quadratic, ½at² − vt + d = 0, with two roots that are both physically real motions ending at the same velocity. The page returns the shorter time and says so; if you know the starting velocity instead, Final Velocity (Uniform Acceleration) gives t without the choice.