Physics Fundamentals

For uniformly accelerated motion, the three equations are: (1) v = u + at, (2) s = ut + (1/2)at^2, (3) v^2 = u^2 + 2as. Here u = initial velocity, v = final velocity, a = acceleration, t = time, s = displacement. Memory aid: 'V-U-A-S' — each equation links four of the five variables, leaving one out. Equation 1 omits s, equation 2 omits v, equation 3 omits t. For a freely falling body, a = g = 9.8 m/s^2 (often taken as 10). For a body thrown up, a = -g. SI unit of acceleration is m/s^2. These are valid ONLY when acceleration is constant.

First Law (Law of Inertia): A body stays at rest or in uniform motion unless an external force acts on it. Explains why passengers jerk forward when a bus brakes. Second Law: Force = mass x acceleration (F = ma); rate of change of momentum equals applied force. Third Law: To every action there is an equal and opposite reaction — e.g. recoil of a gun, rocket propulsion, swimming. Memory aid: 'Inertia, Force, Reaction' = 1-2-3. SI unit of force is newton (N); 1 N = 1 kg.m/s^2. The second law is the most quantitative and is the real definition of force.

A car moving at 20 m/s decelerates at 4 m/s^2. Find the distance before it stops. Using v^2 = u^2 + 2as with v = 0, u = 20, a = -4: 0 = 400 + 2(-4)s, so 8s = 400, giving s = 50 m. Shortcut for stopping distance: s = u^2 / (2a) = 400/8 = 50 m. Time to stop: v = u + at gives 0 = 20 - 4t, t = 5 s. Note: stopping distance is proportional to the SQUARE of speed — doubling speed quadruples the distance, a key road-safety fact often asked in RPF exams.

Work (W) = Force x displacement x cos(theta); W = Fs when force and motion are in the same direction. SI unit: joule (J) = N.m. Kinetic energy KE = (1/2)mv^2; Potential energy PE = mgh. Power = Work/time = W/t, SI unit watt (W) = J/s. Also Power = Force x velocity. Memory aid: 'WET-PoW' — Work = Force x distance, Energy stored, Power = rate of doing work. Commercial unit of electrical energy is the kilowatt-hour (kWh) = 1 unit = 3.6 x 10^6 J. 1 horsepower (HP) = 746 W.

Energy can neither be created nor destroyed; it can only be transformed from one form to another. The total energy of an isolated system remains constant. For a freely falling body, PE continuously converts to KE while total (PE + KE) stays constant. Examples: in a hydroelectric plant PE of water becomes KE then electrical energy; in a pendulum energy swings between KE (at lowest point) and PE (at extremes). Common transformations: electric bulb (electrical to light + heat), microphone (sound to electrical), solar cell (light to electrical), battery (chemical to electrical). This is one of the most frequently tested principles.

A pump lifts 600 kg of water to a height of 10 m in 20 seconds. Find its power (g = 10 m/s^2). Work done = mgh = 600 x 10 x 10 = 60,000 J. Power = Work/time = 60,000 / 20 = 3,000 W = 3 kW. To convert to horsepower: 3000 / 746 = approximately 4 HP. Tip: when a numerical gives mass, height and time together, you are almost always being asked for power via P = mgh/t. Always check the unit demanded (W, kW, or HP) before selecting the answer.

Three common scales: Celsius (C), Fahrenheit (F), and Kelvin (K). Conversions: C/5 = (F-32)/9, and K = C + 273.15 (often 273). Water freezes at 0 C = 32 F = 273 K and boils at 100 C = 212 F = 373 K. Kelvin is the SI unit; 0 K is absolute zero, the lowest possible temperature. Memory aid: 'C-five, F-minus-32-nine'. Quick fact: -40 degrees is the same on both Celsius and Fahrenheit scales. Normal human body temperature is 37 C = 98.6 F. Always convert to Kelvin for gas-law problems.

Heat travels by three modes. Conduction: transfer through direct contact without movement of the material (mostly in solids/metals) — e.g. a metal spoon getting hot in tea. Convection: transfer by actual movement of heated fluid (liquids and gases) — e.g. sea breeze, boiling water, room heater warming air. Radiation: transfer through electromagnetic waves needing NO medium — e.g. heat from the Sun reaching Earth, warmth from a fire. Memory aid: 'Con-tact, Cur-rents, Rays' for Conduction, Convection, Radiation. Radiation is the only mode that works in vacuum, which is why Sun's heat reaches us through empty space.

Specific heat (c) is the heat needed to raise 1 kg of a substance by 1 degree C; Q = mc(delta T). Water has an unusually high specific heat (4186 J/kg.C), so it heats and cools slowly — moderating climate near seas. Latent heat is the heat absorbed or released during a change of state at constant temperature. Latent heat of fusion of ice = 334 J/g (melting); latent heat of vaporization of water = 2260 J/g (boiling). This is why steam at 100 C causes far more severe burns than boiling water at 100 C — it releases extra latent heat on condensing. Temperature stays constant during melting and boiling.

Reflection: light bounces off a surface; angle of incidence = angle of reflection. Refraction: light bends when passing between media of different densities (e.g. a pencil looking bent in water). Light bends TOWARDS the normal entering a denser medium, AWAY when entering a rarer one. Plane mirror forms a virtual, erect, same-size image (laterally inverted). Concave mirror (converging) is used in shaving mirrors, torches and headlights; convex mirror (diverging) gives a smaller, erect image and a wider field of view — used as vehicle rear-view mirrors. Memory aid: 'ConCAVE = CAVE inward = magnify; ConVEX = bulge out = wider view'.

Speed of light in vacuum = 3 x 10^8 m/s (the universe's speed limit; nothing travels faster). Light needs no medium and travels fastest in vacuum. Speed of sound in air at 20 C is about 343 m/s (commonly 330-340). Sound NEEDS a material medium — it cannot travel through vacuum, which is why space is silent. Sound travels FASTEST in solids, slower in liquids, slowest in gases (opposite of light). Memory aid: 'Light loves emptiness, Sound needs matter.' Wave equation: speed v = frequency (f) x wavelength (lambda). This relation applies to all waves.

An echo is reflected sound. To hear a distinct echo, the reflecting surface must be at least about 17 m away (so the sound takes at least 0.1 s to return). Frequency is measured in hertz (Hz). The audible range for humans is 20 Hz to 20,000 Hz. Below 20 Hz is infrasonic (e.g. produced by earthquakes, elephants); above 20,000 Hz is ultrasonic (e.g. used by bats, dolphins, and in sonography/SONAR). Pitch depends on frequency (higher frequency = higher pitch); loudness depends on amplitude. SONAR uses ultrasound to measure ocean depth and detect objects underwater.