Physics Equations - GCSE Physics

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Students should be able to select and apply the following equations from the Physics equation sheet.

Equations required for Higher Tier papers only are indicated by HT in the left hand column.

Equation number	Word equation	Symbol equation
1	weight = mass × gravitational field strength (g)	$W = m\,g$
2	work done = force × distance (along the line of action of the force)	$W = F\,s$
3	force applied to a spring = spring constant × extension	$F = k\,e$
4	moment of a force = force × distance (normal to direction of force)	$M = F\,d$
5	pressure = force normal to a surface ÷ area of that surface	$p = \frac{F}{A}$
6	distance travelled = speed × time	$s = v\,t$
7	acceleration = change in velocity ÷ time taken	$a = \frac{\Delta v}{t}$
8	resultant force = mass × acceleration	$F = m\,a$
9 HT	momentum = mass × velocity	$p = m\,v$
10	kinetic energy = 0.5 × mass × (speed)²	$E_k = \tfrac{1}{2}\,m\,v^2$
11	gravitational potential energy = mass × gravitational field strength (g) × height	$E_p = m\,g\,h$
12	power = energy transferred ÷ time	$P = \frac{E}{t}$
13	power = work done ÷ time	$P = \frac{W}{t}$
14	efficiency = useful output energy transfer ÷ total input energy transfer
15	efficiency = useful power output ÷ total power input
16	wave speed = frequency × wavelength	$v = f\,\lambda$
17	charge flow = current × time	$Q = I\,t$
18	potential difference = current × resistance	$V = I\,R$
19	power = potential difference × current	$P = V\,I$
20	power = (current)² × resistance	$P = I^2\,R$
21	energy transferred = power × time	$E = P\,t$
22	energy transferred = charge flow × potential difference	$E = Q\,V$
23	density = mass ÷ volume	$\rho = \frac{m}{V}$

Equation number	Word equation	Symbol equation
1 HT	pressure due to a column of liquid = height of column × density of liquid × gravitational field strength (g)	$p = h\,\rho\,g$
2	(final velocity)² – (initial velocity)² = 2 × acceleration × distance	$v^2 - u^2 = 2\,a\,s$
3 HT	force = change in momentum ÷ time taken	$F = \frac{m\,\Delta v}{\Delta t}$
4	elastic potential energy = 0.5 × spring constant × (extension)²	$E_e = \tfrac{1}{2}\,k\,e^2$
5	change in thermal energy = mass × specific heat capacity × temperature change	$\Delta E = m\,c\,\Delta\theta$
6	period = 1 ÷ frequency	$T = \frac{1}{f}$
7	magnification = image height ÷ object height
8 HT	force on a conductor (at right angles to a magnetic field) carrying a current = magnetic flux density × current × length	$F = B\,I\,l$
9	thermal energy for a change of state = mass × specific latent heat	$E = m\,L$
10 HT	potential difference across primary coil ÷ potential difference across secondary coil = number of turns in primary coil ÷ number of turns in secondary coil	$\frac{V_p}{V_s} = \frac{n_p}{n_s}$
11 HT	potential difference across primary coil × current in primary coil = potential difference across secondary coil × current in secondary coil	$V_p\,I_p = V_s\,I_s$
12	For gases: pressure × volume = constant	$p\,V = \text{constant}$