Quick start
- Select a mode (SUVAT / projectile / free-fall).
- Pick a preset and tweak numbers (units are shown next to each input).
- Press “Compute” to see results, steps, and the plot. Use “Copy shareable URL” to share the same scenario.
Results
How it’s calculated
Plot
Surface key teaching points, common pitfalls, and reminders for classroom demonstrations.
How to use this mechanics calculator
Choose one of the three motion models first: SUVAT for constant acceleration, projectile motion for two-dimensional launch problems, or free fall for vertical motion under gravity. Then enter the known values and solve for one unknown at a time.
How it works
SUVAT mode selects the constant-acceleration equation that isolates your target variable. Projectile mode resolves the launch speed into horizontal and vertical components, solves the flight-time roots, and reports range, apex time, and maximum height. Free-fall mode solves the vertical quadratic and explains which time root is physically valid.
When to use each mode
Use SUVAT when acceleration stays constant along one line of motion. Use projectile mode when horizontal motion is uniform but vertical motion is accelerated by gravity. Use free-fall mode when you only need vertical position, impact time, and impact velocity.
Common mistakes to avoid
- Mixing the sign convention for up and down halfway through a problem.
- Entering gravity as a negative number when the page already applies the minus sign in the equation.
- Forgetting that projectile mode may produce two time roots and only the non-negative landing time is physically useful.
- Changing unit selections after entering values without checking the converted inputs.
Worked interpretation
If a projectile launched at 20 m/s and 45° looks wrong, first verify the angle unit, then check the starting height and gravity value. For a free-fall problem, compare the reported impact time with the quadratic roots shown in the steps to confirm why the negative root was rejected.
See also
FAQ
How does the SUVAT mode pick a formula?
The tool inspects the known variables and chooses the simplest equation that isolates the unknown, logging the substitutions, algebra, discriminant, and which root (t ≥ 0) is selected.
What outputs are provided in the projectile mode?
It resolves v₀, reports flight time, range, peak height, time to apex, logs both roots of y(t)=0, and renders the trajectory with apex and landing markers.
What inputs are enough to solve a SUVAT problem?
Enter any three compatible quantities and choose exactly one unknown. The page then picks the simplest constant-acceleration equation or quadratic route needed to isolate that missing value.
Why can projectile or free-fall mode show two time roots?
Vertical motion is solved from a quadratic equation, so two mathematical roots can appear. The physically meaningful answer is usually the non-negative time that matches the launch and landing setup shown in the steps.
What does the plot show?
The graph visualizes position over time for the selected motion model. In projectile mode it highlights the apex and landing point; in free-fall mode it helps you verify whether the reported impact time matches the motion you intended.