Kinematics
Use SUVAT-style relationships for displacement and acceleration. Free online calculator with formulas and step-by-step solutions.
Key formula
v = u + at, s = ut + (1/2)at^2, v^2 = u^2 + 2as
How do you solve kinematics (SUVAT) problems?
List known values among s, u, v, a, t, then pick an equation that includes the unknown and omits what you do not have: v = u + at, s = ut + ½at², v² = u² + 2as, or s = ½(u + v)t. Solve algebraically, then check units and signs.
About this tool
Constant-acceleration motion uses the SUVAT equations. This page keeps the core set visible so you can pick the equation that matches the knowns — without forcing everything through average velocity alone.
How to use this calculator
- Choose the variable you want to solve for and confirm which values are already known.
- Enter inputs in consistent units before calculating so the formula is applied correctly.
- Check whether the result is physically reasonable by comparing it with the size of the inputs.
- Use the step-by-step breakdown to see how the equation was rearranged and evaluated.
Worked examples
Example 1: v = u + at
u = 5.0 m/s, a = 2.0 m/s², t = 4.0 s. v = 5 + (2)(4) = 13 m/s.
Example 2: s = ut + ½at²
u = 0, a = 3.0 m/s², t = 5.0 s. s = 0 + ½(3)(25) = 37.5 m.
Example 3: v² = u² + 2as
u = 10 m/s, v = 0, a = −2.0 m/s² (braking). 0 = 100 + 2(−2)s → 4s = 100 → s = 25 m.
Frequently asked questions
What are the SUVAT equations?
The usual set is v = u + at, s = ut + ½at², v² = u² + 2as, and s = ½(u + v)t. They assume constant acceleration.
How do I choose the right kinematics equation?
Write the knowns and the unknown. Choose the equation that contains the unknown and does not require a quantity you were not given. See the SUVAT choice guide on this site for a full walkthrough.
When can I not use SUVAT?
When acceleration is not constant — for example significant air resistance, or motion that needs calculus. Also do not force average-velocity-only methods when a and t are the real drivers.
How do signs work in kinematics?
Pick one direction as positive. Deceleration opposite that direction is negative a. Displacement opposite the positive axis is negative s.
How is this different from v = d/t?
v = d/t is average speed/velocity when you only have distance and time. SUVAT handles changing velocity under constant a. Use the velocity calculator for simple averages; use kinematics when a is involved.