# STEM Physics — Kinematics Velocity-Time Graph Tutor Kinematics visualisation tutor: velocity-time curve (constant-acceleration SUVAT solver with displacement-area shading), projectile parabola (adjustable g + air-resistance toggle), and free-fall timing > Canonical page: https://elysiatools.com/en/tools/education-stem-physics-kinematics-velocity-time-graph - **Category:** Education - **Keywords:** kinematics, velocity-time graph, suvat, projectile motion, free fall, physics, stem, ap physics, acceleration, displacement ## Overview For high-school/university physics students, AP/IB Physics candidates, and K-12 teachers preparing material. Constant-acceleration mode: plots v(t)=u+a·t, shades the area under the curve to make displacement s=∫v dt=ut+½at² visible, and lists all SUVAT quantities. Projectile mode: traces the parabola x=v₀cosθ·t, y=v₀sinθ·t−½gt², gives range / max height / flight time, with optional quadratic air drag. Free-fall mode: time and impact velocity from height and g. Gravity is adjustable (Earth/Moon/Mars). Pure local, deterministic, no network. ## Inputs - **Mode** (select) - **Initial velocity u (m/s)** (number): e.g. 0 (from rest), 5 - **Acceleration a (m/s²)** (number): e.g. 9.81 (free fall), 2 - **Time duration t (s)** (number): e.g. 4 - **Launch speed (m/s)** (number): launch speed, e.g. 20 - **Launch angle θ (°)** (number): e.g. 45 - **Initial height y₀ (m)** (number): e.g. 0 - **Drop height (m)** (number): drop height, e.g. 45 - **Gravity g (m/s²)** (number): Earth 9.81 · Moon 1.62 · Mars 3.72 - **Air resistance** (checkbox) ## When to use - Use the velocity-time mode to study constant acceleration and see displacement as the shaded area under v(t). - Use the projectile mode to compare launch angles, gravity values, range, maximum height, and flight time. - Use the free-fall mode to calculate falling time and impact velocity from a drop height and gravitational acceleration. ## How it works - Choose Velocity-time graph, Projectile trajectory, or Free-fall timing. - Enter the values required for the selected mode, such as u, a, t, launch speed, angle, height, or gravity. - The tool applies the relevant kinematics equations and generates a visual HTML result. - Review the graph and calculated quantities, including displacement, trajectory measures, fall time, or impact velocity. ## Use cases - High-school, AP, and IB Physics practice with visual kinematics graphs. - University mechanics exercises involving SUVAT equations and displacement. - Teacher demonstrations comparing Earth, Moon, and Mars gravity or projectile conditions. ## Frequently asked questions ### What does the velocity-time mode calculate? It plots v(t)=u+a·t, shades the area representing displacement, and lists the SUVAT quantities. ### What results are provided for projectile motion? The tool traces the trajectory and reports range, maximum height, and flight time. ### Can I change the gravitational acceleration? Yes. Enter a gravity value such as Earth’s 9.81 m/s², the Moon’s 1.62 m/s², or Mars’s 3.72 m/s². ### Does the projectile mode include air resistance? Yes. You can enable the Air resistance option for the projectile calculation. ### What inputs are needed for free-fall timing? 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