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2 The speed distance - time equation. d = distance travelled, in metres (m) v = average velocity, in metres per second (m/s) t = time taken for trip, in seconds (s) This equation is only used when the velocity is constant, or for an average velocity. If the velocity is changing, use the area under a speed time graph to calculate distance.
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4 To calculate constant or average acceleration. a = acceleration of object, in metres per second per second (m/s 2 ) Δv = change in velocity of object, in metres per second (m/s) t = time for change in velocity to occur, in seconds (s) Use this equation when the question gives you a change in speed, rather than initial and final speeds.
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6 To calculate constant or average acceleration. a = acceleration of object, in metres per second per second (m/s 2 ) v = final velocity of object, in metres per second (m/s) u = initial velocity of object, in metres per second (m/s) t = time for change in velocity to occur, in seconds (s) Acceleration is the rate of change of velocity.
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8 To calculate the weight of an object. W = weight of object, in Newton (N) m = mass of object, in kilograms (kg) g = gravitational field strength, in newton per kilogram (N/kg) Weight is a force. The weight of an object is the force on it due to a planet s gravitational pull. If an object weighs 100 N on Earth, it weighs 0 N in space (no gravity) and 16 N on the moon. Gravitational field strength of a planet is the weight per unit mass of an object on that planet. The value of g on Earth is 10 N/kg. The mass of an object is the amount of stuff in the object. The mass remains constant anywhere in the universe. An object with mass 10 kg on earth will have a mass of 10 kg in space and a mass of 10 kg on the moon.
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10 The equation for Newton s Second Law. F = unbalanced force acting on body, in newton (N) m = mass of body, in kilograms (kg) a = acceleration of body, in metres per second per second (m/s 2 ) The unbalanced force is the resultant of all forces acting on a body. Forces can change the shape, speed and direction of motion of an object. When the force stays constant and the mass increases, the acceleration decreases. When the mass stays constant and the force increases, the acceleration increases.
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12 To calculate work done by a force. Ew = work done, in joules (J) or newton metres (Nm) F = force applied, in newton (N) d = distance moved by force, in metres (m) Work done is a measure of energy transferred.
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14 To calculate change in gravitational potential energy. Ep = change in gravitational potential energy, in joules (J) m = mass, in kilograms (kg) g = gravitational field strength, in newton per kilogram (N/kg) h = vertical height moved, in metres (m) Gravitational potential energy is the energy required to move a mass upwards through a height. It is also the energy transferred when an object drops though a height. In this case, the energy is usually converted to kinetic energy.
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16 To calculate kinetic energy. Ek = kinetic energy of the body, in joules (J) m = mass of the body, in kilograms (kg) v = velocity of the body, in metres per second (m/s) Kinetic energy is the energy possessed by moving objects. Note: only the velocity is squared not the mass!
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18 To calculate the power of both mechanical and electrical systems. P = power, in watts (W) E = energy transferred, in joules (J) t = time taken, in seconds (s) Power is the energy transferred in one second. Power can also be expressed in joules per second (J/s).
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20 To calculate energy efficiency. useful Eo = useful energy output, in joules (J) Ei = total energy input, in joules (J) The Law on Conservation of Energy states that energy can be neither created nor destroyed. However, only some of the energy changed in a process is useful. The rest is usually wasted as heat. An energy efficient light bulb has an efficiency of around 50%. Half of the electrical energy input comes out as light, the rest is wasted mainly as heat.
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22 To calculate power efficiency. percentage efficiency = efficiency of system, in %. useful Po = useful output power, in watts (W) Pi = input energy, in watts (W)
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24 To calculate the energy transfer for substances changing temperature. The substance does not change state. Eh = energy transferred in changing temperature of substance, in joules (J) c = specific heat capacity of substance, in joules per kilogram per degree Celsius (J/kg 0 C) m = mass of substance, in kilograms (kg) ΔT = change in temperature of substance, in degree Celsius ( 0 C) For water, c = 4180 J/kg 0 C. This means that it takes 4180 J of energy to heat up 1 kg of water by 1 0 C. Or, 1 kg of water will give out 4180 J of energy if it cools by 1 0 C.
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26 To calculate the energy transfer for substances changing state. The temperature remains constant. Eh = energy needed to change state, in joules (J) m = mass which changed state, in kilograms (kg) l = specific latent heat, in joules per kilogram (J/kg) A substance has 2 specific latent heats: lv = specific latent heat of vaporisation (for boiling/condensing) lf = specific latent heat of fusion (for melting/solidifying) For water, lv = 3.34 x 10 5 J/kg; lf = 2.26 x 10 6 J/kg This means that it takes 3.34 x 10 5 J of energy to change 1 kg of water to steam. Or, 1 kg of steam will give out 3.34 x 10 5 J of energy when condensing to water.
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28 To calculate the amount of charge transferred in an electrical circuit. Q = charge transferred, in coulombs (C) I = current, in amperes (A) t = time taken for charge to transfer, in seconds (s)
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30 Also known as Ohm s Law equation. V = voltage across resistance, in volts (V) I = current through resistance, in amperes (A) R = resistance, in ohms (Ω)
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32 To calculate the total resistance of resistances in series. RT = total resistance of circuit, in ohms (Ω) R1 = resistance of first resistor, in ohms (Ω) R2 = resistance of second resistor, in ohms (Ω) In a series circuit, the total resistance is the sum of the individual resistances. R1 R2
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34 To calculate the total resistance of resistors in parallel. RT = total resistance of circuit in ohms (Ω) R1 = resistance of first resistor in ohms (Ω) R2 = resistance of second resistor in ohms (Ω) R1 R2
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36 The equation for voltage dividers in electronic control circuits. V2 = voltage across second resistor, in volts (V) Vs = supply voltage, in volts (V) R1 = resistance of first resistor, in ohms (Ω) R2 = resistance of second resistor, in ohms (Ω)
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38 The equation for voltage dividers. V1 = voltage across first resistor, in volts (V) V2 = voltage across second resistor, in volts (V) R1 = resistance of first resistor, in ohms (Ω) R2 = resistance of second resistor, in ohms (Ω)
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40 To calculate the power in an electrical circuit. P = power in watts (W) I = current in amperes (A) V = voltage in volts (V)
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42 To calculate the power in an electrical circuit. P = power, in watts (W) I = current, in amperes (A) R = resistance, in ohms (Ω)
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44 To calculate the power in an electrical circuit. P = power, in watts (W) V = voltage, in volts (V) R = resistance, in ohms (Ω)
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46 The equation for transformers. ns = number of turns in secondary coil (no units) np = number of turns in primary coil (no units) Vs = voltage in secondary coil, in volts (V) Vp = voltage in primary coil, in volts (V) Ip = current in primary coil, in amperes (A) Is = current in secondary coil, in amperes (A) Transformers are used to reduce power losses in electrical transmission in the National Grid. This is done by operating the transmission lines at a high voltage. Transformers which increase voltage are called step-up transformers. Transformers which reduce voltage are called step-down transformers.
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48 To calculate the voltage gain of an electronic system. Vgain = voltage gain as a fraction (no units) VO = output voltage, in volts (V) VI = input voltage, in volts (V)
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50 To calculate the power gain of an electronic system. Pgain = power gain as a fraction (no units) PO = output power, in watts (W) PI = output power, in watts (W)
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52 Known as the Wave Equation. v = velocity of wave, in metres per second (m/s) f = frequency of wave, in hertz (Hz) λ (lambda) = wavelength, in metres (m) The frequency of a wave is the number of waves that pass a point every second: frequency = number of waves time The velocity of a wave is the distance travelled by the wave every second: velocity = distance travelled time taken
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54 To calculate the power of a lens. P = power of lens, in dioptres (D) f = focal length of lens, in metres (m) Connex lenses have a positive power. Concave lenses have a negative power. Rays parallel to normal
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56 To calculate radioactive activity. A = radioactive activity, in becquerels (Bq) N = number of decays (counts) (no units) t = time taken, in seconds (s) One becquerel is an activity of 1 decay per second.