Equations

Question 1

Kinematics Equations.

Answer 1

v=u+at
s=ut+1/2at^2​
v^2​ ​=u^2​ ​+2as

Question 2

Dynamics Equations.

Answer 2

p=mv
W=mg
F=ma
Δp=F x Δt
m​1u​​1+​m​2u​​2=​m​1v​​1+​m​2v​​2
u​1-​u​2=​v​2-​v​1
Average force= (final momentum-initial momentum)/time

Question 3

Forces Equations.

Answer 3

P=F/A
Pressure of static fluid= ​p​gh
F=kx
EPE of a spring=1/2 k x^2​
Moment of a force= F x d

Question 4

Work, Energy, Power Equations.

Answer 4

F=F x s(cosθ)
KE=1⁄2 mv^2​
GPE=mgh
KE​initial+​PE​initial+​E​supplied=​KE​final+​PE​final+​E​lost
P=Fv
Efficiency=(useful energy input/energy input) x 100%

Question 5

Circular Motion Equations.

Answer 5

T=2𝜋/ω
f=ω/2𝜋
F=ma​ć=​mv^2​​/r=mrω^2​

Question 6

Gravitational Field Equations.

Answer 6

F=GMm/r^2​
g=GM/r^2​
U=-GMm/r
ɸ=-GM/r
F=-dU/dr
g=-dɸ/dr
T^2​ ​ ∝ r^3​

Question 7

Oscillation Equations.

Answer 7

v​ò=​x​òω​
a​ò=x​òω​^2
v=±ω√(x​ò​^2-x​^2)
a=-ω^2​ ​x

Question 8

Waves Equations.

Answer 8

v=fλ
ɸ/2π=Δd/λ
ɸ/2π=Δt/T
I = P/A (area)
E∝A^2​ (amplitude)
I∝A^2​
I=I​ò c​os^2(​​θ)

Question 9

Superposition Equations.

Answer 9

Path difference (Constructive interference)=nλ
Path difference (Destructive interference)=(n+1⁄2)λ
λ=ax/D
d sinθ=nλ
sinθ=λ/b

Question 10

Temperature And Ideal Gas Equations.

Answer 10

θ=(X​θ-​ X​0)​ /(X​100-​ X​0)​ x 100%
T/°C=T/K-273.15
pV=nRT
pV=NkT
1⁄2 m^2​ ​=3/2 kT
U(KE of ideal gas)=​3/2NkT=3/2nRT=3/2pV

Question 11

First Law of Thermodynamics Equations.

Answer 11

Q=mcΔθ
L=​Q/m (latent heat of fusion and vaporisation)
ΔU=Q​in+​W​on

Question 12

Electric field Equations.

Answer 12

F​=​(1/4πε)(Qq/r^2​​)
E=(1/4πε)(Q/r^2​ ​)
E=F/q
U​E=​Qq/4πεr
V=Q/4πεr
E=-dV/dr
E=ΔV/d
F​E=​qE

Question 13

Current of Electricity Equations.

Answer 13

Q=It
I=dQ/dt
I=nAqv
R=V/I
P=W/t=IV=I^2​ ​R=V^2​ ​/R
E=Ir+IR

Question 14

D.C. Circuit Equations.

Answer 14

R​eff=​R​1+​R​2
R​eff=​1/R​1​+1/R​2
V​out=​ R​1/​ R​1+​ R​2​ x V​in

Question 15

Electromagnetism Equations.

Answer 15

B=μ​oI​/2𝜋d
B=μ​oN​I/2r
B=μ​oN​I
F=BILsinθ
F=Bqvsinθ

Question 16

Electromagnetic Induction Equation.

Answer 16

ɸ=BAcosθ
Φ=Nɸ=NBAcosθ
ε=-dΦ/dt=-d(Nɸ)/dt=-d(NBAcosθ)/dt
ε=Blv

Question 17

Alternating Current Equations.

Answer 17

I​rms=​I​o/​2 (square root 2)
V​rms=​V​o/​2 (square root 2)
P​ave=​(I​rms)^​2​​R=(V​rms)​^2​​/R
V​s/​V​p=​I​p/​I​s=​N​s/​N​p
V​pI​​p=​ V​sI​s+​ power loss

Question 18

Quantum Physics Equations.

Answer 18

E=hf=hc/λ
E=ɸ+1⁄2 mv​max2​
ɸ=hf​ò
1⁄2 mv​max2​ ​=eV​s
Intensity=n(hf)/time x area
λ​db=​h/mv
ΔxΔp≥h
ΔEΔt≥h

Question 19

Nuclear Physics Equations.

Answer 19

Mass defect=total mass of constituent protons and neutrons-mass of nucleus Mass defect=total mass of constituent protons and neutrons and electrons-mass of atom
E=mc2​
Binding energy per nucleon=B.E./A
Energy released=(total BE of products-total BE of reactants)
x=x​òe​^-​λt​ where x can be N, A or C
t​1/2=​ln2/λ (t half life)
x/x​ò=​(1⁄2)n​