Physics · Mechanics
Kinematics calculator.
Type any three of displacement, initial velocity, final velocity, acceleration and time. Leave the other two empty and the calculator solves them with the constant-acceleration equations.
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The constant-acceleration equations
For constant acceleration in a straight line, five quantities are linked by two independent equations, so any three of them fix the other two. The equations are v = u + at, s = ut + ½at², s = ½(u + v)t and v² = u² + 2as (OpenStax writes the first and last as v = v0 + at and v² = v0² + 2a(x − x0)). The calculator picks the right pair for whichever three you enter.
Worked example. A car starts from rest (u = 0) and accelerates at 9.8 m/s² for 3 s: v = 29.4 m/s and s = 44.1 m.
Two answers. When you give u, a and s, v² = u² + 2as has a positive and a negative root. A ball thrown at u = 5 m/s with a = −2 m/s² reaches s = 4 m twice: at t = 1 s moving at v = 3 m/s, and again at t = 4 s on the way back at v = -3 m/s. Both are shown; solutions with negative time are discarded.
Use one sign convention: positive in the direction of u, so deceleration and downward gravity are negative if up is positive. Units are not converted, so keep metres and seconds together.
Frequently asked questions
What are the SUVAT equations?
v = u + at, s = ut + ½at², s = ½(u + v)t, v² = u² + 2as and s = vt − ½at². They apply only when acceleration is constant.
How many values do I need to enter?
Exactly three of the five. Leave the other two blank and they are calculated.
Why do I get two solutions?
When you enter u, a and s (or v, a and s) the squared equation has two roots. In the example the object passes s = 4 m at 1 s and again at 4 s.
Can I use this for free fall?
Yes. Use a = 9.8 (or −9.8 with up as positive) and enter the other values. For a drop from rest the free fall calculator is quicker.
What if acceleration is not constant?
These equations then do not apply. Split the motion into stages with constant acceleration, or use calculus.
Sources
Checked
- OpenStax University Physics Volume 1, 3.4 Motion with Constant Acceleration
- OpenStax University Physics Volume 1, 3.5 Free Fall
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Scope
Idealised textbook model for constant acceleration in a straight line. Not for engineering or safety design. Results are arithmetic from the formulas shown, for study and general interest, and not professional or engineering advice.