# Physics Kinematics Problem Solver Solve 1D constant-acceleration kinematics problems and 2D projectile motion, with a full step-by-step derivation. Enter any 3 of the 5 quantities (displacement, initial velocity, final velocity, acceleration, time) and the solver finds the other two, showing each formula, the substitution, and the result. For projectiles, enter launch speed/angle/height to get range, time of flight, and max height. > Canonical page: https://elysiatools.com/en/tools/physics-kinematics-problem-solver - **Category:** Science & Education - **Keywords:** physics, kinematics, suvat, projectile motion, acceleration, velocity, displacement, equations of motion, mechanics, free fall, trajectory, physics homework, newton ## Overview A kinematics solver for high-school and college physics students and teachers: 1. **Problem mode** — choose 1D kinematics (constant acceleration) or 2D projectile motion. 2. **1D: enter 3 of 5** — fill in any three of displacement (Δx), initial velocity (v₀), final velocity (v), acceleration (a), and time (t). The solver finds the other two. 3. **Derivation** — every solved quantity shows the formula used, the substitution with your numbers, and the final value, so you can follow (and check) the working. 4. **Projectile** — enter launch speed, angle, and launch height (plus optional gravity for non-Earth worlds) to get range, flight time, max height, and velocity components. 5. **Impossibility checks** — the solver flags physically impossible inputs (negative v², no real time root, etc.) instead of silently giving nonsense. The five SUVAT equations drive the 1D solver. No external data — pure algebra. ## Inputs - **Problem mode** (select) - **Displacement (Δx, m)** (number): leave blank if unknown - **Initial velocity (v₀, m/s)** (number): leave blank if unknown - **Final velocity (v, m/s)** (number): leave blank if unknown - **Acceleration (a, m/s²)** (number): leave blank if unknown (9.81 for gravity) - **Time (t, s)** (number): leave blank if unknown - **Launch angle (θ, °)** (number): Projectile mode: launch angle above horizontal. - **Launch height (y₀, m)** (number): Projectile mode: initial height above ground. - **Decimal places** (number): 3 ## When to use - When solving 1D constant-acceleration physics homework problems and you need to verify your algebraic steps. - When analyzing 2D projectile trajectories to find range, flight time, maximum height, and velocity components. - When checking for physical impossibilities in kinematics scenarios, such as negative squared velocities or non-real time roots. ## How it works - Select the problem mode: either 1D kinematics (constant acceleration) or 2D projectile motion. - For 1D mode, input any three of the five SUVAT variables (displacement, initial velocity, final velocity, acceleration, or time). For 2D mode, input the launch speed, angle, height, and acceleration. - Set your desired decimal precision and run the solver to generate the results along with the step-by-step formulas and substitutions. ## Use cases - Verifying homework solutions for high school or college-level physics mechanics assignments. - Designing physics exam questions with precise, mathematically consistent kinematics parameters. - Simulating projectile trajectories for game development or physics demonstrations to determine range and flight time. ## Frequently asked questions ### What is SUVAT? SUVAT refers to the five key variables of motion: displacement (s), initial velocity (u), final velocity (v), acceleration (a), and time (t). ### How many variables do I need to enter for 1D kinematics? You must enter exactly three of the five variables to solve for the remaining two. ### Can I change the acceleration due to gravity? Yes, you can adjust the acceleration parameter to simulate gravity on other planets or custom acceleration values. ### What happens if I enter physically impossible values? The solver performs impossibility checks and flags errors like negative squared velocities or non-real time roots instead of returning invalid results. ### Does the solver show the formulas used? Yes, it provides a full step-by-step derivation showing the specific kinematic formulas and substitutions used to reach the final values. ## Related tools - [Mendelian Punnett Square Calculator](https://elysiatools.com/en/tools/mendelian-punnett-square): Build a Punnett square for a Mendelian cross and auto-calculate genotype and phenotype ratios. 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