Physics Equations
Physics Equations
1. Mechanics (Motion, Forces, and Energy)
1.1 Kinematics (Motion)
Describes the motion of objects without considering forces.
| Equation | Description | Example |
|---|---|---|
| $ v = u + at $ | Final velocity ($ v \() after time (\) t \() with acceleration (\) a $) | A car accelerates from 10 m/s at 2 m/s² for 5 s. Find $ v \(. <br> **\) v = 10 + (2 ) = 20 $ m/s** |
| $ s = ut + at^2 $ | Displacement ($ s $) after time $ t $ | A ball drops from rest under gravity for 3 s. Find $ s \(. <br> **\) s = 0 + (9.8)(3)^2 = 44.1 $ m** |
| $ v^2 = u^2 + 2as $ | Final velocity squared | A car starts at 5 m/s, accelerates at 3 m/s², and moves 20 m. Find $ v \(. <br> **\) v^2 = 5^2 + 2(3)(20) = 125 $, $ v = 11.18 $ m/s** |
1.2 Newton’s Laws of Motion
Describes how forces affect motion.
| Equation | Description | Example |
|---|---|---|
| $ F = ma $ | Force ($ F \() is mass (\) m \() times acceleration (\) a $) | A 10 kg object accelerates at 5 m/s². Find $ F \(. <br> **\) F = 10 = 50 $ N** |
| $ p = mv $ | Momentum ($ p \() is mass times velocity | A 2 kg ball moving at 4 m/s has momentum **\) 2 = 8 $ kg·m/s** | |
| $ F t = m v $ | Impulse is force times time | A 0.5 kg ball hits a wall and bounces back with the same speed of 10 m/s. Force applied for 0.2 s is $ F = (0.5 )/0.2 = 50 $ N |
1.3 Work, Energy, and Power
| Equation | Description | Example |
|---|---|---|
| $ W = Fd $ | Work done by force $ F $ over displacement $ d $ | A force of 50 N moves an object 10 m at an angle of 30°. $ W = 50 ° = 433 $ J |
| $ KE = mv^2 $ | Kinetic energy | A 3 kg object moving at 5 m/s has $ KE = 37.5 $ J |
| $ PE = mgh $ | Gravitational potential energy | A 2 kg object at 5 m has $ PE = 2 = 98 $ J |
| $ P = $ | Power is work per time | A machine does 1000 J in 2 s. Power is $ 500 $ W |
2. Electricity and Magnetism
2.1 Electric Circuits
| Equation | Description | Example |
|---|---|---|
| $ V = IR $ | Ohm’s Law (Voltage, Current, Resistance) | A 10Ω resistor with 5A current has $ V = 10 = 50V $ |
| $ P = VI $ | Power in an electric circuit | A 230V appliance draws 2A. Power is $ 460W $ |
| $ Q = It $ | Charge is current times time | A 2A current flows for 5s. Charge is $ 10C $ |
2.2 Magnetism
| Equation | Description | Example |
|---|---|---|
| $ F = BIL $ | Force on a wire in a magnetic field | A 2m wire with 3A in a 0.5T field at 90° has $ F = 3N $ |
| $ = B A $ | Magnetic flux | A 0.1m² loop in a 2T field at 90° has $ = 0.2 $ Wb |
3. Electromagnetic Waves & Optics
3.1 Wave Equations
| Equation | Description | Example |
|---|---|---|
| $ v = f$ | Wave speed | A 500Hz sound wave in air ($ v = 340 $ m/s) has $ = 0.68 $ m |
| $ I = $ | Intensity of a wave | A 100W light source emitting over 10m² has $ I = 10 $ W/m² |
3.2 Optics (Reflection & Refraction)
| Equation | Description | Example |
|---|---|---|
| $ n_1 _1 = n_2 _2 $ | Snell’s Law | Light moving from air ($ n = 1.0 \() to water (\) n = 1.33 \() at 30° bends at **\) _2 = 22° $** |
4. Thermodynamics
| Equation | Description | Example |
|---|---|---|
| $ Q = mcT $ | Heat energy change | Heating 1 kg of water by 10°C takes $ Q = 4184 = 41.84 $ kJ |
| $ PV = nRT $ | Ideal gas law | A gas at 300K with $ 2 $ moles in 0.1m³ has $ P = 4.92 $ kPa |
5. Relativity
| Equation | Description | Example |
|---|---|---|
| $ E = mc^2 $ | Energy-mass equivalence | 1kg of mass converts to $ 9 ^{16} $ J |
6. Quantum Physics
| Equation | Description | Example |
|---|---|---|
| $ E = hf $ | Photon energy | A 500 THz photon has energy $ 3.32 ^{-19} $ J |
7. Nuclear Physics
| Equation | Description | Example |
|---|---|---|
| $ N = N_0 e^{-t} $ | Radioactive decay | If $ = 0.1 $ and $ N_0 = 1000 \(, after 10s: **\) N = 368 $** |