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Physics 1: free practice, theory and problems

The equations of motion describe motion with constant acceleration, for example free fall and a car braking.

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Motion
Forces and Newton's laws
Energy and work
Electricity
Atoms, radiation and the universe

1. Motion

What is it about?

The equations of motion describe motion with constant acceleration, for example free fall and a car braking.

Concepts and formulas

Speed: $v = \dfrac{\Delta s}{\Delta t}$ . Acceleration: $a = \dfrac{\Delta v}{\Delta t}$ .
$v = v_0 + at$
$s = v_0t + \tfrac12 at^2$
$v^2 - v_0^2 = 2as$
$s = \dfrac{v_0 + v}{2}t$
Free fall: $a = g = 9.81\ \text{m/s}^2$ (without air resistance).

Write down what you know (

v_0

v

a

s

t

) and pick the equation that lacks what you do not know.

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2. Forces and Newton's laws

What is it about?

Newton's laws explain how forces change motion.

Concepts and formulas

Newton's 1st law: if the sum of forces is zero, the velocity is constant (or the body is at rest).
Newton's 2nd law: $\sum F = ma$ .
Newton's 3rd law: if A acts on B with a force, B acts on A with an equal and opposite force.
Weight: $G = mg$ . Friction: $R = \mu N$ .
Circular motion: centripetal acceleration $a = \dfrac{v^2}{r}$ .

Draw all the forces, find the sum, use

\sum F = ma

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3. Energy and work

What is it about?

Energy can neither be created nor destroyed, only converted from one form to another. Work is energy transferred by a force.

Concepts and formulas

Work: $W = F s \cos\alpha$ .
Kinetic energy: $E_k = \tfrac12 mv^2$ . Potential energy: $E_p = mgh$ .
Without friction, mechanical energy is conserved: $E_k + E_p$ is constant. Fall from height $h$ : $v = \sqrt{2gh}$ .
Power: $P = \dfrac{W}{t}$ . Efficiency: $\eta = \dfrac{\text{useful energy}}{\text{energy supplied}}$ .

Energy conservation:

\tfrac12 mv^2 = mgh

gives

v = \sqrt{2gh}

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4. Electricity

What is it about?

Electric current is charge in motion. The voltage drives the current, and the resistance opposes it.

Concepts and formulas

Ohm's law: $U = RI$ .
Power: $P = UI = RI^2 = \dfrac{U^2}{R}$ .
Series: $R = R_1 + R_2 + \dots$ , the same current through all.
Parallel: $\dfrac{1}{R} = \dfrac{1}{R_1} + \dfrac{1}{R_2} + \dots$ , the same voltage across all.
Energy: $E = Pt$ (1 kWh = 3.6 MJ).

U = RI

. Series: add. Parallel: add the reciprocals.

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5. Atoms, radiation and the universe

What is it about?

Atomic nuclei can be unstable and emit radiation. Light from stars and galaxies tells us what they are made of and how the universe evolves.

Concepts and formulas

Alpha radiation (helium nuclei), beta radiation (electrons or positrons) and gamma radiation (high-energy photons).
Half-life $T_{1/2}$ : the time it takes for half of the nuclei to decay. Remaining after time $t$ : $N = N_0 \left(\tfrac12\right)^{t/T_{1/2}}$ .
Photon energy: $E = hf = \dfrac{hc}{\lambda}$ , with $h = 6.63 \cdot 10^{-34}$ Js and $c = 3.00 \cdot 10^{8}$ m/s.
Line spectra: every element has its own "fingerprint" of wavelengths.
Redshift and Hubble's law show that the universe is expanding.

Half-life: divide by 2 for each half-life that has passed.

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Example problems with solutions

Here are some of the problems in physics 1. In the app, calculation problems get new numbers every time, so you can practise until it sticks – and take a graded practice exam before the real one.

Motion: A car drives at 90 km/h. How many m/s is that?

Answer: 25 m/s

Divide by 3.6: $90/3.6 = 25$ m/s.

Forces and Newton's laws: A lift moves upwards at constant speed. What is the sum of the forces on it?

Answer: Zero

Constant velocity means zero acceleration, so $\sum F = 0$ (Newton's 1st law).

Energy and work: The speed is doubled. What happens to the kinetic energy?

Answer: It is quadrupled

$E_k = \tfrac12 mv^2$ : double the speed gives four times the energy.

Electricity: What is the total resistance of 10 Ω and 10 Ω in parallel?

Answer: 5 Ω

$1/R = 1/10 + 1/10 = 2/10$ , so $R = 5$ Ω.

Practise all the problems →

Physics 1: free practice, theory and problems

Contents

1. Motion

What is it about?

Concepts and formulas

2. Forces and Newton's laws

What is it about?

Concepts and formulas

3. Energy and work

What is it about?

Concepts and formulas

4. Electricity

What is it about?

Concepts and formulas

5. Atoms, radiation and the universe

What is it about?

Concepts and formulas

Example problems with solutions