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ECAT: Physics, Chemistry and Maths Relations

Flashcards with the key physics, chemistry and mathematics relations used in the ECAT engineering entry test in Pakistan. Original study material.

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Equations of uniform acceleration

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Equations of uniform acceleration

v = u + a t

s = u t + \frac{1}{2} a t^{2}

v^{2} = u^{2} + 2 a s

Kinetic energy and gravitational potential energy

\frac{1}{2} m v^{2}

and

m g h

Power from force and speed

P = F v

Hooke's law and spring energy

F = k x

and

E = \frac{1}{2} k x^{2}

Period of a simple pendulum

T = 2 π L / g

Period of a mass on a spring

T = 2 π m / k

Wave speed

v = f λ

Ohm's law

V = I R

Resistors in series and parallel

R = R_{1} + R_{2}

and

\frac{1}{R} = \frac{1}{R _{1}} + \frac{1}{R _{2}}

Electrical power

P = V I = I^{2} R = V^{2} / R

Coulomb's law

F = \frac{k q _{1} q _{2}}{r ^{2}}

, with

k = 9 \times 1 0^{9} N m^{2} / C^{2}

Capacitor charge and energy

Q = C V

and

E = \frac{1}{2} C V^{2}

Force on a current-carrying wire

F = B I L sin θ

Transformer equation

\frac{V _{s}}{V _{p}} = \frac{N _{s}}{N _{p}}

Heat needed to change temperature

Q = m c Δ T

Snell's law

n_{1} sin θ_{1} = n_{2} sin θ_{2}

Lens formula

\frac{1}{f} = \frac{1}{u} + \frac{1}{v}

Radioactive decay

N = N_{0} (\frac{1}{2})^{t / T}

Moles from mass

n = \frac{m}{M}

Ideal gas law

P V = n R T

Molar volume of a gas at STP

22.4 dm³/mol

Dilution formula

M_{1} V_{1} = M_{2} V_{2}

pH and pOH

p H = - lo g [H^{+}]

and

p H + pO H = 14

at 25 °C

Derivative of

x^{n}

n x^{n - 1}

Quadratic formula

x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

Determinant of a 2×2 matrix

a d - b c

Eccentricity of an ellipse

e = \frac{a ^{2} - b ^{2}}{a} < 1

Distance from a point to a line

\frac{∣ a x _{0} + b y _{0} + c ∣}{a ^{2} + b ^{2}}

Focus of the parabola

y^{2} = 4 a x

(a, 0)

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