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Physics

Uniformly Accelerated Motion

UAM equations. Free online Uniformly Accelerated Motion. Calculate uniformly accelerated motion online — fast, accurate, mobile-friendly, no signup needed.

Final velocity
25 m/s
Displacement
150 m

Derivation

  1. ├── 01Givenu = 5, a = 2, t = 10
  2. ├── 02FormulaFinal velocity: e.u+e.a × e.t
  3. ├── 03Substitutee.5+e.2 × e.10
  4. ├── 04Compute Final velocity25 m/s
  5. ├── 05FormulaDisplacement: t × n+.5 × a × n²
  6. ├── 06Substitute10 × n+.5 × 2 × n²
  7. └── 07Compute Displacement150 m
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§01What is

Understanding the Uniformly Accelerated Motion

The Uniformly Accelerated Motion computes Final velocity from 3 inputs: u (m/s), a (m/s²), t (s). UAM equations.

Physics is the toolkit for turning a real-world observation into a prediction. Whether it’s a falling object, a moving car, or a stressed beam, the equations here are the same ones every engineer relies on. The Uniformly Accelerated Motion sits in that toolkit — it UAM equations. Enter your numbers above and the result updates instantly; every step of the math is shown in the Derivation panel so you can see exactly how the answer was reached.

§02The Formula

How it’s calculated

Final velocity = e.u+e.a × e.t | Displacement = t × n+.5 × a × n²

Where

u
u (m/s)
a
a (m/s²)
t
t (s)
Final velocity
Output value — in m/s
Displacement
Output value — in m
§03Practical Example

Step-by-step walkthrough

Scenario

Apply the formula to a realistic set of inputs: u (m/s) = 5, a (m/s²) = 2, t (s) = 10.

  1. 01Start by noting the input — u (m/s): 5.
  2. 02Start by noting the input — a (m/s²): 2.
  3. 03Start by noting the input — t (s): 10.
  4. 04Substitute these values into the formula: Final velocity = e.u+e.a × e.t | Displacement = t × n+.5 × a × n²
  5. 05Compute Final velocity: the calculator returns 25 m/s.
  6. 06Compute Displacement: the calculator returns 150 m.
  7. 07Cross-check the answer by opening the Derivation panel above — every line of math is shown so you can follow the computation end-to-end.
§04Variants

Common Uniformly Accelerated Motion Problems

The formula gets rearranged depending on which variable you need. Here are the patterns you’ll run into in the real world — find the one that matches your problem and follow the worked steps.

01 · PATTERN

u (m/s) halved

u = 2.5 (from 5)

Keep every other input at its default and halve the u (m/s). See how final velocity responds.

  1. 01New u (m/s): 2.5
  2. 02Baseline Final velocity: 25 m/s
  3. 03New Final velocity: 22.5 m/s
  4. 04Final velocity decreases by 10% → use this sensitivity to plan for real-world variation.
02 · PATTERN

u (m/s) doubled

u = 10 (from 5)

Keep every other input at its default and double the u (m/s). See how final velocity responds.

  1. 01New u (m/s): 10
  2. 02Baseline Final velocity: 25 m/s
  3. 03New Final velocity: 30 m/s
  4. 04Final velocity increases by 20% → use this sensitivity to plan for real-world variation.
03 · PATTERN

a (m/s²) halved

a = 1 (from 2)

Keep every other input at its default and halve the a (m/s²). See how final velocity responds.

  1. 01New a (m/s²): 1
  2. 02Baseline Final velocity: 25 m/s
  3. 03New Final velocity: 15 m/s
  4. 04Final velocity decreases by 40% → use this sensitivity to plan for real-world variation.
04 · PATTERN

a (m/s²) doubled

a = 4 (from 2)

Keep every other input at its default and double the a (m/s²). See how final velocity responds.

  1. 01New a (m/s²): 4
  2. 02Baseline Final velocity: 25 m/s
  3. 03New Final velocity: 45 m/s
  4. 04Final velocity increases by 80% → use this sensitivity to plan for real-world variation.
§05FAQ

Frequently asked questions

Yes. The calculator implements the standard formula as documented and returns exact floating-point results. No approximations are used unless noted in the formula.
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