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 is deliberately not offered here. Rearranged for t it becomes a quadratic, ½at² − vt + d = 0, with two roots that are both physically real — the moment the object passes a point on the way out and the moment it passes the same point on the way back. Rather than silently pick one, use Final Velocity (Uniform Acceleration) or Displacement (Uniform Acceleration), which solve for t unambiguously.