Motion is described by distance, speed, velocity and acceleration. Graphs turn those quantities into pictures you can read.
➡️ Speed, velocity and acceleration
Speed = distance ÷ time.Velocity is speed in a given direction. Acceleration = change in velocity ÷ time, measured in m/s². With constant acceleration a from a start speed u, the speed after time t is v = u + at. Falling objects near Earth’s surface accelerate at g = 10 m/s² when air resistance is ignored.
150 m in 30 s → speed = 150 / 30 = 5 m/s
0 → 24 m/s in 6 s → a = 24 / 6 = 4 m/s²
dropped from rest: v = gt = 10 × 3 = 30 m/s after 3 s
average speed = total distance / total time
100 m in 20 s then 100 m in 30 s → 200 / 50 = 4 m/s
🖼️ See it
A steeper slope means a greater speed; a flat line means the object is at rest.
📈 Reading motion graphs
On a distance–time graph, the slope is the speed; a flat line means the object is at rest. On a velocity–time graph, the slope is the acceleration and the area under the line is the distance travelled.
distance–time: line from (0 s, 0 m) to (10 s, 50 m)
speed = 50 / 10 = 5 m/s
velocity–time: constant 10 m/s for 6 s
area = 10 × 6 = 60 m
straight sloping line = constant acceleration
flat line on a v–t graph = constant velocity
Check the axes first. The same slope means speed on one graph and acceleration on another.
🧪 Worked examples: journeys on a speed–time graph
A three-stage journey. A car speeds up from rest to 20 m/s in 5 s, travels at 20 m/s for 10 s, then brakes to a stop in 5 s. Split the area under the graph into shapes.
stage 1 triangle ½ × 5 × 20 = 50 m
stage 2 rectangle 20 × 10 = 200 m
stage 3 triangle ½ × 5 × 20 = 50 m
total distance = 300 m in 20 s
average speed = 300 ÷ 20 = 15 m/s (less than the top speed)
Stopping distance. It is the sum of the thinking distance (travelled during the reaction time, at constant speed) and the braking distance.
speed 20 m/s, reaction time 0.7 s
thinking distance = 20 × 0.7 = 14 m
braking distance (from the graph) = 40 m
stopping distance = 14 + 40 = 54 m
Free fall from rest with g = 10 m/s² and no air resistance.
falls for 3 s: v = g t = 10 × 3 = 30 m/s
height = ½ g t² = 5 × 9 = 45 m
Shape of a distance–time graph. A straight sloping line is constant speed. A curve getting steeper is accelerating. A curve getting flatter is decelerating. A horizontal line is stationary.
🎯 Exam focus: describing and calculating from graphs
When asked to describe a graph, say what happens in each section with numbers: “Between 5 s and 15 s the car travels at a constant speed of 20 m/s.” Then calculate the gradient or area, and show the working.
gradient of a speed–time graph = acceleration = Δv ÷ Δt
area under a speed–time graph = distance
gradient of a distance–time graph = speed
braking from 20 m/s to 0 in 5 s: a = (0 − 20) ÷ 5 = −4 m/s² (deceleration of 4 m/s²)
Common mistakes. Taking the average speed as the average of the first and last speeds when the journey has a stop. Reading the gradient of a distance–time graph as acceleration. Mixing minutes with seconds. Forgetting that velocity is a vector: a negative velocity means the opposite direction. Measuring the area of a triangle without the ½.
Units. 1 m/s = 3.6 km/h. 72 km/h ÷ 3.6 = 20 m/s.
✏️ Quick check · 1 of 11
Velocity
Velocity differs from speed because it includes:
It is a vector.
✏️ Quick check · 2 of 11
d–t slope
On a distance–time graph, a horizontal line means the object is:
No change in distance.
✏️ Quick check · 3 of 11
v–t slope
On a velocity–time graph, the slope of the line is:
Rise over run.
✏️ Quick check · 4 of 11
Free fall
Ignoring air resistance, a falling object near Earth’s surface:
Acceleration is constant.
✍️ Type your answer · 5 of 11
A runner covers 150 m in 30 s.
What is the speed, in m/s?
Enter an exact answer, without rounding.
m/s
speed = distance ÷ time.
✍️ Type your answer · 6 of 11
A car accelerates from rest to 24 m/s in 6 s.
What is the acceleration, in m/s²?
Enter an exact answer, without rounding.
m/s²
a = change in velocity ÷ time.
✍️ Type your answer · 7 of 11
A cyclist travels 100 m in 20 s, then 100 m in 30 s.
What is the average speed for the whole trip, in m/s?
Enter an exact answer, without rounding.
m/s
Total distance ÷ total time.
✍️ Type your answer · 8 of 11
A car accelerates from rest to 20 m/s in 5 s, travels at 20 m/s for 10 s, then brakes to rest in 5 s.
What total distance does it travel, in metres?
Enter an exact answer, without rounding.
m
Split the area into two triangles and a rectangle.
✍️ Type your answer · 9 of 11
The journey takes 20 s in total and covers 300 m.
What is the average speed, in m/s?
Enter an exact answer, without rounding.
m/s
Total distance divided by total time.
✍️ Type your answer · 10 of 11
A driver travelling at 20 m/s has a reaction time of 0.7 s.
What is the thinking distance, in metres?
Enter an exact answer, without rounding.
m
The car moves at constant speed during the reaction time.
✏️ Quick check · 11 of 11
Distance–time graph
On a distance–time graph, a curve that becomes steeper and steeper shows an object that is:
Gradient = speed.
📝 Lesson quiz · 5 questions
0 / 5
Re-read the lesson, then give it another go.
Question 1 of 5
The unit of acceleration is:
Question 2 of 5
The area under a velocity–time graph gives:
Question 3 of 5
A car moves at a steady 20 m/s for 10 s. The distance covered is:
Question 4 of 5
A sloping straight line on a velocity–time graph shows:
Question 5 of 5
An object dropped from rest has a speed after 2 s of (g = 10 m/s²):
Lesson 2 · Dynamics
💪 Forces & Newton’s Laws
Forces change motion. Newton’s three laws describe how, and F = ma lets you calculate it.
⚖️ Net force and F = ma
The net force is the vector sum of all forces. Newton’s first law: with zero net force an object keeps its velocity (rest or constant speed in a straight line). The second law: F = ma, so the same force gives a smaller acceleration to a larger mass. Weight = mass × g, a force in newtons, while mass is in kilograms.
5 kg accelerated at 3 m/s²: F = 5 × 3 = 15 N
weight of 60 kg: W = 60 × 10 = 600 N
forward 50 N, friction 20 N → net force = 30 N
mass 10 kg → a = 30 / 10 = 3 m/s²
🖼️ See it
Together the laws describe how forces change motion.
↔️ Action–reaction and terminal velocity
Newton’s third law: when A pushes on B, B pushes back on A with an equal and opposite force. The two forces act on different objects, so they do not cancel. A falling object speeds up until air resistance equals its weight; then the net force is zero and it falls at terminal velocity.
rocket pushes gas down → gas pushes rocket up
skydiver: weight 800 N downward
terminal velocity when air resistance = 800 N upward
net force = 0, acceleration = 0
Zero acceleration is not zero velocity. A skydiver at terminal velocity is still moving fast.
🧪 Worked examples: resultant force, springs and moments
Resultant force. Forces in opposite directions subtract. Then use F = ma.
car mass 1200 kg, engine force 3000 N, air resistance 600 N
resultant = 3000 − 600 = 2400 N
a = F ÷ m = 2400 ÷ 1200 = 2 m/s²
Hooke’s law. Within the limit of proportionality, force is proportional to extension: F = k x.
a 5 N load stretches a spring by 2 cm (0.02 m)
k = 5 ÷ 0.02 = 250 N/m
a 8 N load: x = 8 ÷ 250 = 0.032 m = 3.2 cm
Moments. Moment = force × perpendicular distance from the pivot. For balance, clockwise moments = anticlockwise moments.
seesaw: 300 N at 1.5 m on the left, an unknown force F at 0.5 m on the right
300 × 1.5 = F × 0.5 → F = 450 ÷ 0.5 = 900 N
Weight on other planets. Mass is constant but weight depends on g. A 60 kg person on the Moon (g = 1.6 N/kg) weighs 60 × 1.6 = 96 N.
🎯 Exam focus: explaining motion with forces
To explain terminal velocity, use a sequence: (1) at the start, weight is bigger than air resistance, so there is a resultant force downward; (2) as speed rises, air resistance rises; (3) at terminal velocity, air resistance equals weight, the resultant force is zero and the speed is constant.
opening the parachute:
air resistance suddenly > weight → resultant upward → deceleration
speed falls → resistance falls → balanced again at a new, lower terminal velocity
Common mistakes. Saying that “no resultant force means no movement” (it means no change in velocity). Writing that a third-law pair acts on the same object (they act on two different objects). Using mass in newtons or weight in kilograms. Measuring the spring’s length instead of its extension. Using the distance along the beam rather than the perpendicular distance from the pivot.
Force diagram. Draw each arrow from the object, label its name and size, and make longer arrows for larger forces.
✏️ Quick check · 1 of 11
First law
A hockey puck slides at constant velocity on frictionless ice. The net force on it is:
No acceleration.
✏️ Quick check · 2 of 11
Mass and weight
Which statement is correct?
Newtons.
✏️ Quick check · 3 of 11
Third law
The reaction to the force of your foot pushing back on the ground is:
Opposite, on the other object.
✏️ Quick check · 4 of 11
Terminal velocity
A skydiver reaches terminal velocity when:
Balanced forces.
✍️ Type your answer · 5 of 11
A 5 kg trolley is pushed with a net force that gives it an acceleration of 3 m/s².
What is the net force, in N?
Enter an exact answer, without rounding.
N
F = ma.
✍️ Type your answer · 6 of 11
What is the weight of a 60 kg person (g = 10 m/s²)?
Give the weight in N.
Enter an exact answer, without rounding.
N
W = mg.
✍️ Type your answer · 7 of 11
A 10 kg box is pushed forward with 50 N against friction of 20 N.
What is its acceleration, in m/s²?
Enter an exact answer, without rounding.
m/s²
Find the net force first.
✍️ Type your answer · 8 of 11
A car of mass 1200 kg has an engine force of 3000 N and air resistance of 600 N.
What is its acceleration, in m/s²?
Enter an exact answer, without rounding.
m/s²
Find the resultant force first.
✍️ Type your answer · 9 of 11
A 5 N load stretches a spring by 2 cm.
What is the spring constant, in N/m?
Enter an exact answer, without rounding.
N/m
Convert the extension to metres.
✍️ Type your answer · 10 of 11
A seesaw is balanced. A 300 N force acts 1.5 m from the pivot on one side. Another force acts 0.5 m from the pivot on the other side.
What is the second force, in newtons?
Enter an exact answer, without rounding.
N
Equate the moments.
✏️ Quick check · 11 of 11
Third law
A book rests on a table. Which force is the third-law pair of the weight of the book (the Earth’s pull on the book)?
Swap the two objects.
📝 Lesson quiz · 5 questions
0 / 5
Re-read the lesson, then give it another go.
Question 1 of 5
If the net force on an object doubles (mass constant), its acceleration:
Question 2 of 5
Newton’s third law forces:
Question 3 of 5
A car rounds a bend at constant speed. It is accelerating because:
Question 4 of 5
The unit of force is the:
Question 5 of 5
Friction acts:
Lesson 3 · Energy
⚡ Work, Energy & Power
Energy is never created or destroyed, only transferred. Work measures the transfer, and power measures how fast it happens.
🔋 Work and energy stores
Work = force × distance moved in the direction of the force (W = Fd, in joules). Kinetic energy is ½mv². Gravitational potential energy is mgh. In a closed system, energy is conserved, though some always spreads to the surroundings as heat.
push 20 N through 5 m: W = 20 × 5 = 100 J
KE of 2 kg at 10 m/s: ½ × 2 × 10² = 100 J
GPE of 3 kg raised 5 m: 3 × 10 × 5 = 150 J
dropped from 5 m: mgh = ½mv² → v² = 2 × 10 × 5 = 100 → v = 10 m/s
🖼️ See it
Doubling the speed quadruples the kinetic energy, because the speed is squared.
🔌 Power and efficiency
Power = work (or energy) ÷ time, in watts (1 W = 1 J/s). Efficiency = useful energy out ÷ total energy in × 100%. No machine is 100% efficient because some energy is always wasted as heat or sound.
600 J in 20 s: P = 600 / 20 = 30 W
lamp: 200 J in, 80 J useful light out
efficiency = 80 / 200 × 100 = 40%
1 kW = 1000 W
Joules measure the amount of energy; watts measure how fast.
🧪 Worked examples: energy transfers and power
Lifting. The work done equals the gain in gravitational potential energy.
crane lifts 200 kg through 15 m in 20 s
W = m g h = 200 × 10 × 15 = 30 000 J
P = W ÷ t = 30 000 ÷ 20 = 1500 W
Falling. With no air resistance, GPE lost = KE gained.
m g h = ½ m v² → v = √(2 g h) = √(2 × 10 × 20) = 20 m/s (from a 20 m drop)
Braking. The kinetic energy is removed by work done by the brakes: Fd = ½mv².
1000 kg car at 20 m/s: KE = ½ × 1000 × 400 = 200 000 J
braking force 5000 N: d = 200 000 ÷ 5000 = 40 m
double the speed → KE × 4 → braking distance × 4
Efficiency.
a motor uses 500 J of electrical energy and lifts a load by 300 J of GPE
efficiency = 300 ÷ 500 × 100 = 60%
the other 200 J is wasted as heat and sound
Energy resources. Fossil fuels (coal, oil, gas) and nuclear fuels are non-renewable. Wind, solar, hydroelectric, tidal, wave and geothermal are renewable.
🎯 Exam focus: describing energy changes
Name the store and the transfer in order: “The chemical energy in the fuel is transferred as heat to the water, which becomes the kinetic energy of the turbine, and then electrical energy in the generator.”
KE = ½ m v² GPE = m g h W = F d P = W ÷ t = E ÷ t
efficiency = useful energy out ÷ total energy in × 100%
energy is conserved, but spreads out and becomes less useful
Common mistakes. Forgetting to square the speed in KE. Saying that energy is “used up” or “lost” (it is transferred to the surroundings, often as heat). Writing the efficiency as more than 100%. Mixing joules and kilojoules, or watts and kilowatts. Using the length of the slope rather than the vertical height for GPE.
Stopping distance link. KE depends on v², so the braking distance goes up by four times when the speed doubles. That is why speed limits matter.
✏️ Quick check · 1 of 11
Energy conservation
Energy in a closed system is:
Neither made nor lost.
✏️ Quick check · 2 of 11
Work
Work is done when:
Force times distance.
✏️ Quick check · 3 of 11
Power
The unit of power is the:
Joule per second.
✏️ Quick check · 4 of 11
Kinetic energy
If an object’s speed doubles, its kinetic energy:
v is squared.
✍️ Type your answer · 5 of 11
A force of 20 N pushes a box 5 m in the direction of the force.
How much work is done, in J?
Enter an exact answer, without rounding.
J
W = Fd.
✍️ Type your answer · 6 of 11
A 2 kg ball moves at 10 m/s.
What is its kinetic energy, in J?
Enter an exact answer, without rounding.
J
KE = ½mv².
✍️ Type your answer · 7 of 11
A lamp takes in 200 J of energy and gives out 80 J as light.
What is its efficiency, in percent?
Enter an exact answer, without rounding.
%
Useful ÷ total.
✍️ Type your answer · 8 of 11
A crane lifts a 200 kg load through 15 m in 20 s. Use g = 10 m/s².
What power does the crane supply to the load, in watts?
Enter an exact answer, without rounding.
W
Work done divided by time.
✍️ Type your answer · 9 of 11
A ball is dropped from a height of 20 m. Ignore air resistance and use g = 10 m/s².
What is its speed just before it hits the ground, in m/s?
Enter an exact answer, without rounding.
m/s
GPE lost = KE gained.
✍️ Type your answer · 10 of 11
A car of mass 1000 kg travels at 20 m/s and brakes with a constant force of 5000 N.
What is the braking distance, in metres?
Enter an exact answer, without rounding.
m
Work done by the brakes equals the KE.
✏️ Quick check · 11 of 11
Renewable energy
Which of these is a non-renewable energy source?
Which one can run out?
📝 Lesson quiz · 5 questions
0 / 5
Re-read the lesson, then give it another go.
Question 1 of 5
The gravitational potential energy of a 3 kg mass raised 5 m (g = 10 m/s²) is:
Question 2 of 5
A motor does 600 J of work in 20 s. Its power is:
Question 3 of 5
A ball falls and bounces back lower each time because:
Question 4 of 5
A machine is 100% efficient if:
Question 5 of 5
Energy stored in a stretched spring is:
Lesson 4 · Thermal physics
🌡️ Heat & Thermal Energy
Heat is energy moving because of a temperature difference. How much a material warms up depends on its mass and its specific heat capacity.
🔥 Heating and specific heat capacity
The thermal energy needed to change the temperature of a substance is Q = mcΔT, where c is the specific heat capacity (energy to warm 1 kg by 1 °C). For water c = 4200 J/(kg·°C), which is why water warms slowly and stores much heat.
2 kg water, 20 °C → 30 °C
Q = 2 × 4200 × 10 = 84 000 J
time with a 2000 W heater = 84 000 / 2000 = 42 s
rearranged: ΔT = Q / (mc)
63 000 J into 1.5 kg of water: ΔT = 63 000 / (1.5 × 4200) = 10 °C
🖼️ See it
On the flat sections the energy goes into breaking bonds between particles, so the temperature does not rise.
🧊 Changes of state and heat transfer
During melting or boiling the temperature stays constant while energy breaks bonds between particles. The energy for a change of state is Q = mL (L = latent heat). Heat moves by conduction (particles vibrating and passing energy along, mainly solids), convection (currents in liquids and gases) and radiation (infrared waves, which need no medium).
melt 0.5 kg ice (L = 340 000 J/kg)
Q = 0.5 × 340 000 = 170 000 J
metal block 0.5 kg warms by 10 °C using 2250 J
c = Q / (mΔT) = 2250 / (0.5 × 10) = 450 J/(kg·°C)
Dark, matt surfaces absorb and emit radiation best; shiny, light ones are poor absorbers.
🧪 Worked examples: heating curves and experiments
Two-stage heating. First change the temperature, then the state.
0.5 kg of water from 20 °C to 100 °C: Q = 0.5 × 4200 × 80 = 168 000 J
time with a 2000 W heater = 168 000 ÷ 2000 = 84 s
boiling 0.1 kg of it away: Q = 0.1 × 2 260 000 = 226 000 J
Melting.
0.2 kg of ice at 0 °C into water at 0 °C
Q = m L = 0.2 × 340 000 = 68 000 J
Finding c by experiment. Heat a block with an electric heater and use E = P t.
50 W heater for 400 s → E = 20 000 J into a 1.0 kg block
temperature rise = 10 K
c = Q ÷ (m ΔT) = 20 000 ÷ (1.0 × 10) = 2000 J/(kg·K)
(in practice, insulate the block, as some heat is lost, so the measured c is a bit too high)
Evaporation. The fastest-moving particles escape, so the average kinetic energy of the liquid falls and the liquid cools. This is how sweating works.
🎯 Exam focus: heat transfer and particle explanations
conduction particles vibrate and pass energy; free electrons in metals make them good conductors
convection warm fluid is less dense and rises; cooler fluid sinks (a current)
radiation infrared waves; no medium needed; black surfaces absorb and emit best, shiny worst
On a heating curve, the flat sections are changes of state: the energy goes into breaking the bonds between particles (potential energy), and the kinetic energy (temperature) stays constant.
Common mistakes. Saying that heat rises (hot fluids rise). Saying that conduction happens in a vacuum. Forgetting to convert grams to kilograms. Using ΔT from the final temperature only. Writing that “temperature” and “heat” are the same: temperature measures the average kinetic energy, while heat is energy transferred.
Insulation. Trapped air reduces conduction and convection, which is why wool and double glazing work well.
✏️ Quick check · 1 of 11
Conduction
Heat moves through a metal spoon mainly by:
Solids.
✏️ Quick check · 2 of 11
Convection
Convection occurs in:
Fluids.
✏️ Quick check · 3 of 11
Radiation
The Sun’s heat reaches Earth by:
Space is a vacuum.
✏️ Quick check · 4 of 11
State change
While ice melts at 0 °C, its temperature:
Constant during the change.
✍️ Type your answer · 5 of 11
2 kg of water is heated from 20 °C to 30 °C (c = 4200 J/(kg·°C)).
How much energy is needed, in J?
Enter an exact answer, without rounding.
J
Q = mcΔT.
✍️ Type your answer · 6 of 11
A 2000 W heater supplies 84 000 J to a kettle of water.
How long does that take, in s?
Enter an exact answer, without rounding.
s
time = energy ÷ power.
✍️ Type your answer · 7 of 11
Melt 0.5 kg of ice at 0 °C (latent heat of fusion 340 000 J/kg).
How much energy is needed, in J?
Enter an exact answer, without rounding.
J
Q = mL.
✍️ Type your answer · 8 of 11
0.5 kg of water is heated from 20 °C to 100 °C. The specific heat capacity of water is 4200 J/(kg·°C).
How much energy is needed, in joules?
Enter an exact answer, without rounding.
J
Q = m c ΔT.
✍️ Type your answer · 9 of 11
A 2000 W heater supplies 168 000 J to the water.
How long does it take, in seconds?
Enter an exact answer, without rounding.
s
Time = energy ÷ power.
✍️ Type your answer · 10 of 11
A 50 W heater warms a 1.0 kg metal block by 10 K in 400 s. Assume no heat loss.
What is the specific heat capacity of the metal, in J/(kg·K)?
Enter an exact answer, without rounding.
J/(kg·K)
First find the energy supplied.
✏️ Quick check · 11 of 11
Sweating
Why does sweating cool the body?
Think about which particles escape.
📝 Lesson quiz · 5 questions
0 / 5
Re-read the lesson, then give it another go.
Question 1 of 5
Which has the highest specific heat capacity?
Question 2 of 5
A vacuum flask reduces heat loss by:
Question 3 of 5
Temperature measures:
Question 4 of 5
When a hot object touches a cold one, thermal energy flows:
Question 5 of 5
Which colour surface is the best emitter of radiation?
Lesson 5 · Waves
🌊 Waves, Sound & Light
Waves carry energy without carrying matter. Sound and light behave as waves, and the same wave equation links them.
〰️ Wave properties
Frequency f is the number of waves per second (hertz). The period is T = 1/f. Wavelength λ is the distance between matching points. Amplitude is the maximum displacement. The wave speed is v = fλ. Waves are transverse (light; vibrations at right angles to travel) or longitudinal (sound; vibrations along the direction of travel).
f = 50 Hz, λ = 2 m → v = 50 × 2 = 100 m/s
f = 250 Hz → T = 1 / 250 = 0.004 s
sound in air: 340 m/s; λ = 0.5 m → f = 340 / 0.5 = 680 Hz
an echo returns after 2 s → distance to wall = 340 × 2 / 2 = 340 m
🖼️ See it
Frequency is the number of waves per second; wave speed = frequency × wavelength.Frequency and energy increase along the spectrum; wavelength decreases. All travel at the speed of light in a vacuum.
🔦 Reflection and refraction
Light reflects with the angle of incidence equal to the angle of reflection, both measured from the normal. When light enters a denser medium it slows down and bends toward the normal: refraction. The refractive index is n = c / v, the speed of light in a vacuum divided by the speed in the material.
incidence 35° → reflection 35°
light in glass travels at 2 × 10⁸ m/s; c = 3 × 10⁸ m/s
n = 3 / 2 = 1.5
white light through a prism: red bends least, violet bends most (dispersion)
Sound cannot travel through a vacuum because it needs particles; light can.
🧪 Worked examples: echoes, refractive index and the spectrum
Echo or sonar. The pulse travels there and back, so use half the time.
ultrasound in sea water, speed 1500 m/s, echo after 0.4 s
depth = 1500 × 0.4 ÷ 2 = 300 m
Refractive index from angles. n = sin i ÷ sin r (air to the material).
sin i = 0.6, sin r = 0.4
n = 0.6 ÷ 0.4 = 1.5
speed in the material = 3.0 × 10⁸ ÷ 1.5 = 2.0 × 10⁸ m/s
The electromagnetic spectrum in order of increasing frequency: radio, microwave, infrared, visible, ultraviolet, X-ray, gamma. All travel at 3.0 × 10⁸ m/s in a vacuum.
radio wave f = 100 MHz = 1.0 × 10⁸ Hz
λ = v ÷ f = 3.0 × 10⁸ ÷ 1.0 × 10⁸ = 3.0 m
Sound. Pitch depends on frequency, loudness on amplitude. Humans hear about 20 Hz to 20 000 Hz; ultrasound is above this.
🎯 Exam focus: diagrams and descriptions
For refraction diagrams: draw the normal as a dashed line, measure both angles from the normal, and show that the ray bends towards the normal entering a denser medium and away when leaving.
total internal reflection needs
1 light travelling from a denser to a less dense medium
2 an angle of incidence greater than the critical angle C
sin C = 1 ÷ n (n = 1.5 → C = 42°) uses: optical fibres, prisms in binoculars
Common mistakes. Measuring angles from the surface instead of from the normal. Saying that waves transfer matter (they transfer energy). Using the full time in an echo calculation. Mixing up amplitude (height) and wavelength (length). Writing that sound travels in a vacuum, and that sound is faster in air than in solids (it is slower).
Danger of EM radiation. Ionising radiation (UV, X-rays, gamma) can damage cells and cause cancer; microwaves heat tissue.
✏️ Quick check · 1 of 11
Transverse
Which is a transverse wave?
Electromagnetic waves.
✏️ Quick check · 2 of 11
Longitudinal
Sound waves are:
Compressions and rarefactions.
✏️ Quick check · 3 of 11
Refraction
When light passes from air into glass it:
It slows down.
✏️ Quick check · 4 of 11
Vacuum
Which cannot travel through a vacuum?
It needs particles.
✍️ Type your answer · 5 of 11
A wave has a frequency of 50 Hz and a wavelength of 2 m.
What is its speed, in m/s?
Enter an exact answer, without rounding.
m/s
v = fλ.
✍️ Type your answer · 6 of 11
Sound (340 m/s) has a wavelength of 0.5 m.
What is its frequency, in Hz?
Enter an exact answer, without rounding.
Hz
f = v ÷ λ.
✍️ Type your answer · 7 of 11
Light travels at 2 × 10⁸ m/s in glass and 3 × 10⁸ m/s in a vacuum.
What is the refractive index of the glass?
Enter an exact answer, without rounding.
n = c ÷ v.
✍️ Type your answer · 8 of 11
Sonar sends a pulse of ultrasound to the sea bed, and the echo returns after 0.4 s. The speed of sound in water is 1500 m/s.
What is the depth of the water, in metres?
Enter an exact answer, without rounding.
m
The pulse travels down and up.
✍️ Type your answer · 9 of 11
Light enters glass with sin i = 0.6 and sin r = 0.4.
What is the refractive index of the glass?
Enter an exact answer, without rounding.
n = sin i ÷ sin r.
✍️ Type your answer · 10 of 11
A radio wave has a frequency of 1.0 × 10⁸ Hz and travels at 3.0 × 10⁸ m/s.
What is its wavelength, in metres?
Enter an exact answer, without rounding.
m
v = f λ.
✏️ Quick check · 11 of 11
Electromagnetic spectrum
Which type of electromagnetic radiation has the highest frequency?
Think of the ionising end.
📝 Lesson quiz · 5 questions
0 / 5
Re-read the lesson, then give it another go.
Question 1 of 5
A ray hits a mirror at 35° to the normal. It reflects at:
Question 2 of 5
The period of a 250 Hz wave is:
Question 3 of 5
Increasing the amplitude of a sound wave makes it:
Question 4 of 5
Increasing the frequency of a sound wave makes it:
Question 5 of 5
Which colour of visible light bends the most in a prism?
Lesson 6 · Electricity
🔌 Electricity & Circuits
Electric current is a flow of charge. Voltage pushes it, resistance opposes it, and the three are linked by Ohm’s law.
🔗 Ohm’s law and resistors
Current I (amperes) is the flow of charge. Voltage V (volts) is the energy per unit charge. Resistance R (ohms). V = IR. In a series circuit, the current is the same everywhere and resistances add: R = R₁ + R₂. In a parallel circuit, the voltage is the same across each branch and the total resistance is less than the smallest branch: 1/R = 1/R₁ + 1/R₂.
V = IR: 12 V across 4 Ω → I = 12 / 4 = 3 A
series: 2 Ω + 3 Ω = 5 Ω
parallel: 6 Ω and 3 Ω
1/R = 1/6 + 1/3 = 1/6 + 2/6 = 3/6 = 1/2 → R = 2 Ω
🖼️ See it
A straight line through the origin means the resistor is ohmic; the slope is the resistance.
💡 Electrical power and energy
Power P = IV (watts). Energy E = Pt. Household energy is billed in kilowatt-hours: 1 kWh is a 1 kW appliance running for 1 hour. Use an ammeter in series and a voltmeter in parallel. A fuse melts if the current is too high, protecting the wiring.
12 V, 3 A → P = 12 × 3 = 36 W
2 kW heater for 3 h = 2 × 3 = 6 kWh
cost at 0.25 per kWh = 6 × 0.25 = 1.50
Never touch mains electricity. Water lowers the resistance of your skin and raises the danger.
🧪 Worked examples: mixed circuits, fuses and cost
Series and parallel together. Simplify the parallel part first.
6 Ω and 3 Ω in parallel: 1/R = 1/6 + 1/3 = 1/2 → R = 2 Ω
then in series with 4 Ω: R_total = 2 + 4 = 6 Ω
supply 12 V: I = V ÷ R = 12 ÷ 6 = 2 A
voltage across the 4 Ω resistor = 2 × 4 = 8 V, leaving 4 V across the parallel pair
Fuse rating. Choose the next fuse above the normal current.
920 W kettle at 230 V: I = P ÷ V = 920 ÷ 230 = 4 A
standard fuses are 3 A, 5 A and 13 A
3 A would blow in normal use; 13 A is too high to protect the kettle’s flex; choose 5 A
Cost of electricity.
3 kW heater for 2 h = 6 kWh
cost at 30 pence per kWh = 6 × 30 = 180 pence = £1.80
Components. A thermistor’s resistance falls as temperature rises. An LDR’s resistance falls as light increases. A diode lets current pass in one direction only.
🎯 Exam focus: safety and circuit rules
series same current everywhere; voltages add up to the supply; R adds
parallel same voltage across branches; currents add up at a junction; R falls
Q = I t charge (coulombs) = current × time
P = I V E = P t V = I R
In a plug, the live (brown) wire carries the current, the neutral (blue) completes the circuit, and the earth (green and yellow) protects the user by carrying a fault current to the ground, so the fuse blows. The fuse goes in the live wire.
Common mistakes. Adding the resistances in parallel instead of using the reciprocal formula. Connecting an ammeter in parallel, or a voltmeter in series. Forgetting to convert kW and hours for the cost. Saying that current is “used up” in a lamp (the energy is transferred; the current is the same on both sides). Giving the unit of charge as the ampere.
Double insulation. Appliances with a plastic case need no earth wire.
✏️ Quick check · 1 of 11
Series current
In a series circuit, the current is:
One path.
✏️ Quick check · 2 of 11
Parallel voltage
In a parallel circuit, the voltage across each branch is:
Same two points.
✏️ Quick check · 3 of 11
Meters
A voltmeter is connected:
Across the component.
✏️ Quick check · 4 of 11
Fuse
The purpose of a fuse is to:
A safety device.
✍️ Type your answer · 5 of 11
A 4 Ω resistor has 12 V across it.
What current flows, in A?
Enter an exact answer, without rounding.
A
V = IR.
✍️ Type your answer · 6 of 11
A 2 Ω resistor and a 3 Ω resistor are in series.
What is the total resistance, in Ω?
Enter an exact answer, without rounding.
Ω
Add them.
✍️ Type your answer · 7 of 11
A 6 Ω and a 3 Ω resistor are in parallel.
What is the total resistance, in Ω?
Enter an exact answer, without rounding.
Ω
Add the reciprocals.
✍️ Type your answer · 8 of 11
A 6 Ω resistor and a 3 Ω resistor are in parallel, and this pair is in series with a 4 Ω resistor.
What is the total resistance of the circuit, in ohms?
Enter an exact answer, without rounding.
Ω
Combine the parallel pair first.
✍️ Type your answer · 9 of 11
A 6 Ω and 3 Ω pair in parallel, in series with a 4 Ω resistor (total 6 Ω), is connected to a 12 V supply.
What is the current from the supply, in amperes?
Enter an exact answer, without rounding.
A
Use V = I R.
✍️ Type your answer · 10 of 11
A 3 kW heater runs for 2 hours. Electricity costs 30 pence per kWh.
What is the cost, in pence?
Enter an exact answer, without rounding.
p
Energy in kWh = power in kW × time in h.
✏️ Quick check · 11 of 11
Fuses
A kettle takes a current of 4 A at 230 V. Which standard fuse should be fitted in its plug?
Choose the next rating above 4 A.
📝 Lesson quiz · 5 questions
0 / 5
Re-read the lesson, then give it another go.
Question 1 of 5
The unit of resistance is the:
Question 2 of 5
A 12 V supply drives 3 A through a lamp. Its power is:
Question 3 of 5
A 2 kW heater runs for 3 hours. The energy used is:
Question 4 of 5
Adding another resistor in parallel makes the total resistance:
Question 5 of 5
An ammeter is connected:
Final Challenge
🏆 12-Question Challenge Quiz
Questions from every topic in this course. Pick an answer for each one, then hit Check My Answers.
0 / 12
💪 Keep practicing — go back through the lessons and retake the quiz!
Q1 · Motion & Graphs
Which pair of quantities are both vectors?
Q2 · Motion & Graphs
An object dropped from rest has a speed after 2 s of (g = 10 m/s²):
Q3 · Forces & Newton’s Laws
An astronaut’s mass on the Moon compared with Earth is:
Q4 · Forces & Newton’s Laws
Friction acts:
Q5 · Work, Energy & Power
A 1 kW heater is on for 1 s. It transfers:
Q6 · Work, Energy & Power
Energy stored in a stretched spring is:
Q7 · Heat & Thermal Energy
Latent heat is the energy needed to:
Q8 · Heat & Thermal Energy
Which colour surface is the best emitter of radiation?
Q9 · Waves, Sound & Light
An echo returns after 2 s. The sound speed is 340 m/s. The wall is:
Q10 · Waves, Sound & Light
Which colour of visible light bends the most in a prism?
Q11 · Electricity & Circuits
If the voltage across a fixed resistor doubles, the current: