The Uniformly Accelerated Motion Calculator solves problems where an object's acceleration stays constant throughout the interval being studied. Enter any three of the five key quantities, displacement, initial velocity, final velocity, acceleration and time, and the tool finds the remaining two using the correct SUVAT equation.
Uniformly accelerated motion is the foundation of introductory mechanics: a car accelerating steadily from a stoplight, a ball in free fall, or a train braking at a constant rate all fit this model as long as the acceleration itself does not change during the interval in question.
Solve any uniformly accelerated motion problem
Five quantities describe constant-acceleration motion along a straight line, and knowing any three of them fixes the other two.
| Symbol | Quantity | SI unit |
|---|---|---|
| s | displacement | metres (m) |
| u | initial velocity | metres per second (m/s) |
| v | final velocity | metres per second (m/s) |
| a | acceleration | metres per second squared (m/s²) |
| t | time | seconds (s) |
Fill in the three known values and leave the remaining two blank. The calculator identifies which equation fits the given combination and solves accordingly, showing the substitution at each step.
Use the four defining equations
Four equations describe uniformly accelerated motion, and each one omits exactly one of the five variables, which is the key to picking the right one for any given problem.
| Equation | Leaves out | Use when missing |
|---|---|---|
| v = u + at | s | displacement |
| s = ut + ½at² | v | final velocity |
| s = ½(u + v)t | a | acceleration |
| v² = u² + 2as | t | time |
Worked example: a car starts at rest and accelerates at 2 m/s² for 3 seconds. Find final velocity and displacement.
1. Apply v = u + at for final velocity. v = 0 + (2 × 3) = 6 m/s.
2. Apply s = ut + ½at² for displacement. s = (0 × 3) + ½(2)(9) = 9 m.
Verify results with a second equation
A useful check on any SUVAT answer is to confirm it with a different equation that uses the same known values plus the newly found unknown.
Continuing the example above, checking displacement with v² = u² + 2as: v² = u² + 2as → 6² = 0² + 2(2)(s) → 36 = 4s → s = 9 m, matching the earlier result exactly.
This cross-check catches most arithmetic slips, since an error in one calculation rarely produces a consistent answer through a second, independent equation.
Know when uniformly accelerated motion applies
The model assumes acceleration is constant, not merely present. Gravity near Earth's surface, ignoring air resistance, is a textbook example of constant acceleration. A car easing off the accelerator gradually, or a rocket burning fuel and losing mass, does not have constant acceleration and needs calculus-based methods instead of the simple SUVAT equations.
Real-world friction and air resistance mean these equations are approximations even for "constant acceleration" scenarios like free fall over long distances, but they hold well enough for the vast majority of introductory physics problems.
Choose consistent sign conventions
Before substituting numbers, decide which direction counts as positive. That choice must remain fixed for every quantity, initial velocity, final velocity and acceleration, throughout the same problem.
Gravity is negative if up is chosen as positive, and a ball thrown upward will show a final velocity that changes sign as it rises, peaks and falls, all while gravity itself stays constant and negative throughout.
Work through a braking example
A car traveling at u = 20 m/s brakes at a = −5 m/s² and comes to a stop. Find the time taken and the distance covered. 1. Apply v = u + at, with v = 0 at the stop. 0 = 20 + (−5)t → t = 20/5 = 4 s.
2. Apply v² = u² + 2as to find displacement. 0² = 20² + 2(−5)s → 0 = 400 − 10s → s = 400/10 = 40 m.
The car takes 4 seconds and covers 40 m while braking to a stop, using two different SUVAT equations that share the same known values of u and a.
Frequently asked questions
What does uniformly accelerated motion mean?
It describes motion where acceleration stays constant, neither speeding up nor slowing down in its rate of change, throughout the interval being studied.
How many SUVAT equations are there?
Four independent equations describe uniformly accelerated motion, each omitting one of the five variables: displacement, initial velocity, final velocity, acceleration and time.
How do I know which equation to use?
Identify which three of the five variables are given, and pick the equation that does not require the two unknowns. Each equation is missing exactly one variable, which determines when it applies.
Can uniformly accelerated motion have negative acceleration?
Yes. Negative acceleration (sometimes called deceleration when it opposes motion) fits the same equations; the sign simply reflects the direction relative to your chosen positive axis.
Does this apply to free fall?
Yes, when air resistance is ignored. Free fall near Earth's surface has essentially constant acceleration, standard gravity at 9.80665 m/s², making it a standard uniformly accelerated motion problem.
What if acceleration is not actually constant?
Then these four equations do not apply directly, and the problem requires calculus-based kinematics that account for a changing acceleration over time.
Can I check my SUVAT answer without redoing the whole problem?
Yes. Substitute your answer into a second equation that uses a different combination of the known values. If both equations agree, your answer is very likely correct.
Summary
Uniformly accelerated motion is governed by four equations connecting displacement, initial velocity, final velocity, acceleration and time, with each equation omitting exactly one variable. A car starting from rest and accelerating at 2 m/s² for 3 seconds reaches 6 m/s and covers 9 m, a result that checks out identically through two independent equations.
The model requires genuinely constant acceleration; anything that changes rate over time needs a different approach.