Physics describes how objects move and why. The same principles that explain a thrown baseball also explain satellite orbits, car crashes, and roller coasters. This guide covers the core concepts of classical mechanics — the physics of motion — with real-world examples and the key equations you need, whether you are studying for a class or just curious about how the world works.
Speed is how fast an object is moving — a scalar quantity with magnitude only. A car traveling at 60 mph has a speed of 60 mph regardless of direction.
Velocity includes both magnitude and direction — it is a vector. A car traveling 60 mph north has a velocity of 60 mph north. Change direction while maintaining speed, and your velocity changes even though your speed does not. Use the Speed Calculator or Average Speed Calculator to work through problems.
Acceleration is the rate of change of velocity over time: a = Δv / Δt. A car that goes from 0 to 60 mph (26.8 m/s) in 6 seconds has an average acceleration of 4.47 m/s². Negative acceleration (deceleration) means the object is slowing down. Even constant-speed circular motion involves acceleration because the direction of velocity is constantly changing.
| Scenario | Speed | Acceleration | Time to Reach Speed |
|---|---|---|---|
| Walking | 1.4 m/s (3.1 mph) | ~0.5 m/s² | ~3 seconds |
| Sprinter (100m) | 10.4 m/s (23.3 mph) | ~4.5 m/s² | ~2.3 seconds (to top speed) |
| Car (0–60 mph) | 26.8 m/s (60 mph) | ~4.5 m/s² | 6 seconds |
| Free fall (gravity) | 9.8 m/s after 1 sec | 9.8 m/s² | Continuous |
| Space shuttle launch | ~7,800 m/s (orbital) | ~30 m/s² (peak) | ~8.5 minutes |
Values are approximate and assume idealized conditions. Air resistance affects all real-world scenarios.
First Law (Inertia): An object at rest stays at rest, and an object in motion stays in motion at constant velocity, unless acted upon by a net external force. This is why you lurch forward when a car brakes suddenly — your body wants to keep moving at the car's original speed. Mass is the measure of inertia: more mass means more resistance to changes in motion.
Second Law (F = ma): The net force on an object equals its mass times its acceleration. This is the most important equation in classical mechanics. A 1,500 kg car accelerating at 3 m/s² requires a net force of 4,500 newtons. Double the mass with the same force, and acceleration halves. This law explains why heavier objects need larger engines to achieve the same acceleration.
Third Law (Action-Reaction): For every force, there is an equal and opposite reaction force. When you stand on the floor, gravity pulls you down (your weight) and the floor pushes you up with exactly equal force (the normal force). When a rocket expels exhaust gases downward, the gases push the rocket upward with equal force.
Real-world F = ma: A 70 kg person jumping exerts a ground reaction force of approximately 1,400 N (about twice body weight). Using F = ma: net upward force = 1,400 N − 686 N (weight) = 714 N. Acceleration = 714 / 70 = 10.2 m/s². This acceleration occurs during the push-off phase (about 0.3 seconds), producing a takeoff velocity of approximately 3.06 m/s and a jump height of about 0.48 meters (19 inches). Use the Gravitational Force Calculator to explore force and mass relationships.
For motion with constant acceleration, four equations describe everything. Given any three quantities, you can solve for the other two:
v = v₀ + at — final velocity equals initial velocity plus acceleration times time.
x = v₀t + ½at² — displacement equals initial velocity times time plus half acceleration times time squared.
v² = v₀² + 2ax — final velocity squared equals initial velocity squared plus twice acceleration times displacement.
x = ½(v₀ + v)t — displacement equals the average velocity times time.
These equations power everything from calculating braking distances to determining how high a ball goes. Use the Speed Distance Time Calculator to solve these relationships quickly.
A projectile is any object moving through the air under the influence of gravity alone (ignoring air resistance). The key insight is that horizontal and vertical motions are independent: gravity only affects the vertical component, while horizontal velocity remains constant.
For a projectile launched at angle θ with initial speed v₀: the horizontal distance (range) is R = (v₀² × sin(2θ)) / g, and the maximum height is H = (v₀² × sin²(θ)) / (2g). The range is maximized at a 45-degree launch angle.
Use the Projectile Motion Calculator to visualize trajectories with different angles and speeds, and the Speed of Sound Calculator to explore how motion relates to wave physics.
Kinetic energy (KE = ½mv²) is energy of motion. Because velocity is squared, doubling speed quadruples kinetic energy. A car moving at 60 mph has four times the kinetic energy of the same car at 30 mph — which is why stopping distance approximately quadruples when speed doubles.
Gravitational potential energy (PE = mgh) is stored energy due to height. A 70 kg person at the top of a 50-meter building has PE = 70 × 9.8 × 50 = 34,300 joules of gravitational potential energy.
The law of conservation of energy states that energy is neither created nor destroyed, only transformed. A roller coaster at the top of a hill has maximum potential energy and minimum kinetic energy. At the bottom, potential energy has converted to kinetic energy. The total remains constant (minus friction and air resistance losses). Use the Kinetic Energy Calculator to explore these relationships.
Visualize trajectories, calculate forces, and solve kinematics problems. Use the free Projectile Motion Calculator to explore physics of motion — no signup required.
Related tools: Speed Calculator · Gravitational Force Calculator · Kinetic Energy Calculator · Momentum Calculator · Speed Distance Time Calculator · Torque Calculator · Newton's Law Calculator