Free tool
Fill in any three of displacement, initial velocity, final velocity, acceleration and time. The calculator solves the other two for constant acceleration and tells you which equation it used.
Built for College Physics I and AP Physics 1Pick one direction as positive and keep it. For free fall with up positive, a = -9.80.
Fill in exactly three values and leave two blank.
Choosing the right kinematic equation is a recall skill. Encodr turns it into spaced-repetition practice so it holds up on exam day.
Get started freeFor constant acceleration, starting the clock at t = 0, with x as the displacement:
(1) x = (v0 + v)t / 2 - no acceleration
(2) v = v0 + at - no displacement
(3) x = v0 t + (1/2)at² - no final velocity
(4) v² = v0² + 2ax - no time
Each equation leaves out one of the five variables. Pick the equation that leaves out the variable you neither know nor need, and it has exactly one unknown. That is all this calculator does: it looks at which two values are blank, uses one equation to get the first unknown, then a second equation for the other.
Equation 4 gives v², so v can be positive or negative. A ball thrown up at 10.0 m/s (a = -9.80 m/s²) is 3.00 m above the launch point twice: once on the way up at 0.365 s moving at +6.42 m/s, and again on the way down at 1.68 s moving at -6.42 m/s. Both are real, so the calculator reports both. Any solution with negative time is dropped, and if the value under the square root is negative (the ball never gets that high) there is no solution.
A car moving at 20.0 m/s brakes at 5.00 m/s² to a stop. Take the direction of motion as positive, so a = -5.00 m/s². Time and distance are unknown. Equation 2 gives t = (0 - 20.0) ÷ (-5.00) = 4.00 s, and equation 4 gives x = (0 - 400) ÷ (2 × -5.00) = 40.0 m. Those are the default inputs above.
The full guide is the four kinematic equations and when to use each. For motion in two dimensions, use the projectile motion calculator, and the whole course is in the free College Physics I deck.
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