Solve any uniform-acceleration motion problem. Enter exactly three of the five kinematic variables and the solver will calculate the remaining two using the equations of motion.
Variables: s = displacement | u = initial velocity | v = final velocity | a = acceleration | t = time. Negative values are valid (e.g. deceleration, downward motion).
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Standard Physics
Classical Newtonian mechanics. Equations apply to constant (uniform) acceleration only.
Enter exactly 3 values to solve (0 entered so far)
1. Known Values
m
m/s
m/s
m/s²
s
2. Quick-Fill Example
Load a preset scenario to see how the solver works.
Equations applied:
All Five Variables
s
Displacement
--
metres
u
Initial velocity
--
m/s
v
Final velocity
--
m/s
a
Acceleration
--
m/s²
t
Time
--
seconds
Worked Solution
Enter three values above to see the step-by-step working.
The Five Kinematic (SUVAT) Equations
The five equations of motion describe the relationship between displacement, velocity, acceleration, and time for an object moving with constant acceleration. They were derived from the definitions of velocity and acceleration and are the foundation of classical mechanics at NCEA, A-Level, and first-year university physics.
Equation
Form
Variable not included
1
v = u + at
s (displacement)
2
s = ut + ½at²
v (final velocity)
3
v² = u² + 2as
t (time)
4
s = ½(u + v)t
a (acceleration)
5
s = vt − ½at²
u (initial velocity)
Each equation omits one variable, so once you know three variables you can always find an equation that contains exactly one unknown and solve it directly. When only three values are known and none of the five single-variable forms applies directly (rare in introductory problems), the solver above uses algebraic substitution between equations.
Worked Example: Default Values
A car travelling at u = 20 m/s brakes with a = -5 m/s² for t = 4 s. Find v and s.
Step 1: Find v using v = u + at
v = 20 + (-5)(4) = 20 - 20 = 0 m/s
Step 2: Find s using s = ut + ½at²
s = 20(4) + ½(-5)(4²) = 80 + ½(-5)(16) = 80 - 40 = 40 m
The car decelerates to rest in 4 seconds, covering 40 metres. This matches the braking scenario preset above.
Sign Convention
You must choose a positive direction and apply it consistently. Common choices:
Horizontal motion: right is positive, left is negative.
Vertical motion: upward is positive, downward is negative (so g = -9.81 m/s²).
Some textbooks define downward as positive when studying falling objects, making g = +9.81 m/s². Either convention works as long as it is consistent throughout the problem.
When SUVAT Does Not Apply
The SUVAT equations require acceleration to be constant throughout the motion. They do not apply when:
Acceleration varies with time (for example, a rocket burning fuel, air resistance proportional to velocity).
The object moves in a circle (acceleration is centripetal and changes direction continuously).
The object experiences a varying force (for example, a spring system in simple harmonic motion).
For non-constant acceleration, you need calculus: integration of the acceleration function to find velocity, and integration again to find displacement.
Sources and method: Equations of motion derived from definitions a = dv/dt and v = ds/dt with constant acceleration. Standard form as used in NCEA Physics (Achieve/Merit/Excellence) and international A-Level syllabi. Values of g = 9.81 m/s² per NIST/BIPM conventions.
This solver applies the five standard kinematic equations and assumes constant (uniform) acceleration throughout the motion. For problems with varying acceleration, projectile motion (two dimensions), or relativistic speeds, additional tools are required. Always verify the sign convention you have chosen is consistent across all variables entered.
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