Formula Library
Every formula, explained
Each entry includes variables, SI units, a worked example, and where it's used in the real world.
Kinematics
First equation of motion
v = u + a·t
Velocity changes linearly with time under constant acceleration.
v Final velocity (m/s)u Initial velocity (m/s)a Acceleration (m/s²)t Time (s)
Example: A car accelerates at 2 m/s² from 5 m/s for 4 s: v = 5 + 2·4 = 13 m/s.
Used in: Vehicle dynamics, free fall, rocket burn phases.
Displacement equation
s = u·t + ½·a·t²
Total displacement under uniform acceleration.
s Displacement (m)u Initial velocity (m/s)a Acceleration (m/s²)t Time (s)
Example: From rest at a = 3 m/s² for 2 s: s = 0 + ½·3·4 = 6 m.
Used in: Braking distance, ballistics, drop tests.
Time-independent equation
v² = u² + 2·a·s
Relates velocities and displacement without involving time.
v Final velocity (m/s)u Initial velocity (m/s)a Acceleration (m/s²)s Displacement (m)
Example: u = 0, a = 9.81, s = 20 → v ≈ 19.81 m/s.
Used in: Free-fall velocity from height.
Mechanics
Newton's Second Law
F = m·a
Net force equals mass times acceleration.
F Net force (N)m Mass (kg)a Acceleration (m/s²)
Example: A 10 kg object at 2 m/s²: F = 20 N.
Used in: Engineering, vehicle design, fluid resistance.
Linear Momentum
p = m·v
Momentum is conserved in any closed system.
p Momentum (kg·m/s)m Mass (kg)v Velocity (m/s)
Example: A 5 kg ball at 4 m/s carries p = 20 kg·m/s.
Used in: Collisions, rocket propulsion, sports physics.
Energy
Kinetic Energy
KE = ½·m·v²
Energy possessed by an object due to motion.
KE Kinetic energy (J)m Mass (kg)v Velocity (m/s)
Example: 2 kg @ 10 m/s → KE = 100 J.
Used in: Collisions, vehicle safety, turbines.
Gravitational Potential Energy
PE = m·g·h
Energy stored by an object at height in a gravitational field.
PE Potential energy (J)m Mass (kg)g Gravity (m/s²)h Height (m)
Example: 1 kg @ 10 m → PE ≈ 98.1 J.
Used in: Hydropower, pendulums, roller coasters.
Gravitation
Newton's Law of Gravitation
F = G·(m₁·m₂)/r²
Every pair of masses attracts with a force inversely proportional to r².
F Force (N)G Gravitational const. (N·m²/kg²)m₁ Mass 1 (kg)m₂ Mass 2 (kg)r Distance (m)
Example: Earth–Moon attraction ≈ 1.98×10²⁰ N.
Used in: Orbital mechanics, tides, astrophysics.
Electricity
Ohm's Law
V = I·R
Voltage across a conductor is proportional to current.
V Voltage (V)I Current (A)R Resistance (Ω)
Example: 2 A through 5 Ω → V = 10 V.
Used in: All electrical circuit design.
Electrical Power
P = V·I
Rate at which electrical energy is transferred.
P Power (W)V Voltage (V)I Current (A)
Example: 230 V @ 2 A → P = 460 W.
Used in: Power ratings, energy bills, motor sizing.
Waves
Wave Speed
v = f·λ
Speed of a wave equals frequency × wavelength.
v Wave speed (m/s)f Frequency (Hz)λ Wavelength (m)
Example: Sound at f = 440 Hz, λ ≈ 0.78 m → v ≈ 343 m/s.
Used in: Acoustics, optics, radio engineering.