Velocity Calculator
Use the velocity calculator to assess how fast an object moves, given a certain distance and time.
The formula
v = u + at, s = ut + ½at², v² = u² + 2as, s = ½(u+v)t
Five equations, three degrees of freedom
Motion at constant acceleration involves five quantities — displacement, initial and final velocity, acceleration and time — connected by four equations, each of which omits one quantity. That structure is what makes the problem tractable: give any three and the other two follow, and the equation to reach for is the one missing the quantity you do not have.
One subtlety this page handles that most do not. When you supply a displacement together with an acceleration that reverses the motion, the body can pass that displacement twice — once going out and once coming back — and both are legitimate answers. A ball thrown upward is at head height on the way up and again on the way down. Where that happens the second solution is reported rather than quietly discarded.
Two cases have no answer at all. Inconsistent values describe no motion. And giving initial velocity, final velocity and an acceleration of zero leaves time completely undetermined, because with no acceleration the velocity never changes and every duration fits equally well.