Example data table
| Scenario | Method | Inputs | Final velocity |
|---|---|---|---|
| Car accelerates forward | v = u + a·t | u=5 m/s, a=2 m/s², t=3 s | 11 m/s |
| Object slows down | v² = u² + 2·a·s | u=20 m/s, a=−4 m/s², s=40 m | 0 m/s |
| Average velocity over interval | v = s / t | s=120 m, t=10 s | 12 m/s |
Formulas used
- v = u + a·t (constant acceleration)
- v² = u² + 2·a·s (constant acceleration, no time)
- v = s / t (average velocity over an interval)
How to use this calculator
- Select the method that matches your known variables.
- Enter values and pick units for each input.
- Choose the output unit and precision.
- Press Calculate to view the result above the form.
- Use Download CSV or Download PDF for reports.
Kinematics inputs and method selection
This tool supports three motion models so you can match the data you measured. When acceleration is constant and time is known, use v = u + a·t. When time is missing but displacement is available, use v² = u² + 2·a·s. For interval-based reporting, use v = s/t.
Unit handling and internal consistency
All calculations are converted to SI internally: velocity in m/s, acceleration in m/s², distance in meters, and time in seconds. Output can be displayed in m/s, km/h, or mph, while input fields accept common laboratory units including ft and minutes.
Direction, signs, and realistic outcomes
The sign of each variable carries direction. A negative acceleration represents deceleration in the chosen positive direction. In the squared-velocity method, the term u² + 2as must be non‑negative for a real velocity. If it becomes negative, the calculator flags the case so you can verify the sign convention or measurement values.
Precision control for reporting
Precision can be set from 0 to 10 decimal places. For classroom work, 2–4 decimals typically fits measurement uncertainty. For simulations or repeated tests, higher precision helps compare small differences while still keeping values readable.
Graphing for quick validation
The interactive plot visualizes your selected model using SI values. For v = u + a·t, the line slope equals acceleration and the intercept equals initial velocity. For v² mode, the curve shows how speed changes with displacement, and the sign option tracks direction. For v = s/t, displacement grows linearly with time using the computed average velocity.
Exports for audit trails
Download options create a compact CSV summary and a printable PDF report from your latest session result. These exports include the method label, final velocity, and the primary input values, which supports lab notebooks, homework submissions, and engineering notes without retyping numbers.
FAQs
Which method should I choose?
Pick the method that matches your known variables: use u, a, t for constant acceleration with time; use u, a, s when time is unknown; use s and t for average velocity reporting.
Why does the v² method ask for a square‑root sign?
Solving v² = u² + 2as gives two roots, +√ and −√. Choose the sign that matches the direction of motion in your coordinate system and the context of the problem.
What does “no real solution” mean?
It means u² + 2as became negative, so the square root is not real. This often happens from inconsistent signs, unit mistakes, or using constant‑acceleration formulas outside valid conditions.
Can I use negative time or distance?
Time should be non‑negative in most physical setups. Distance can be negative if you define displacement opposite to your positive direction. Use signs consistently across u, a, and s.
Does the calculator compute instantaneous velocity for v = s/t?
No. v = s/t provides average velocity over the chosen interval. If acceleration varies during the interval, the average may differ from the instantaneous velocity at the end.
What gets included in the CSV and PDF exports?
Exports include the method label, final velocity in your output unit, and the main inputs that were provided. They reflect the latest successful calculation stored in the current session.