Kinematics Calculator

What is Kinematics?

Kinematics is the branch of physics that describes the motion of objects without considering the forces that cause the motion. It focuses on quantities like displacement, velocity, acceleration, and time.

The Four Kinematic Equations

For motion with constant acceleration, there are four fundamental equations:

1. Velocity-Time Equation

v = v₀ + at

This equation relates final velocity (v) to initial velocity (v₀), acceleration (a), and time (t).

2. Displacement-Time Equation

Δx = v₀t + ½at²

This equation calculates displacement (Δx) from initial velocity, acceleration, and time.

3. Velocity-Displacement Equation

v² = v₀² + 2aΔx

This equation relates velocities to acceleration and displacement, without involving time.

4. Average Velocity Equation

Δx = ½(v₀ + v)t

This equation calculates displacement using the average of initial and final velocities.

Key Variables Explained

• Δx (Displacement): The change in position (meters, m)
• v₀ (Initial Velocity): Velocity at the start (meters per second, m/s)
• v (Final Velocity): Velocity at the end (meters per second, m/s)
• a (Acceleration): Rate of velocity change (meters per second squared, m/s²)
• t (Time): Duration of motion (seconds, s)

How to Use This Calculator

1. Select the equation: Choose which kinematic equation to use based on your known values
2. Enter known values: Input the values you know
3. View results: Get instant results with step-by-step explanation

When to Use Each Equation

Example Problems

Free Fall

A ball is dropped from rest. What is its velocity after 3 seconds?

• v₀ = 0 m/s, a = 9.8 m/s², t = 3 s
• v = 0 + (9.8)(3) = 29.4 m/s

Car Braking

A car traveling at 20 m/s brakes with -5 m/s² acceleration. How far does it travel before stopping?

• v₀ = 20 m/s, v = 0 m/s, a = -5 m/s²
• v² = v₀² + 2aΔx → 0 = 400 + 2(-5)Δx → Δx = 40 m

Real-World Applications

• Free fall calculations: Gravity problems (g = 9.8 m/s²)
• Vehicle motion: Acceleration, braking, and stopping distances
• Projectile motion: Rockets, thrown objects, sports physics
• Engineering design: Conveyor systems, elevators, machinery
• Crash analysis: Forensic physics and accident reconstruction

Important Assumptions

These equations only apply when:

• Acceleration is constant throughout the motion
• Motion is in a straight line (1D motion)
• For 2D motion, apply equations separately to x and y components

Common Acceleration Values

Sign Conventions

• Positive direction: Usually right or upward
• Negative acceleration: Slowing down (deceleration) or acceleration in negative direction
• Free fall: Use positive g if down is positive, negative g if up is positive