IGCSE Physics Notes · Chapter 2

Motion

Speed, velocity and acceleration, how to read and draw motion graphs, and why a falling skydiver stops speeding up.

✓ Free chapter Syllabus 1.2 Core + Extended 10-question quiz
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Syllabus Contents 2.1 Speed 2.2 Average speed 2.3 Velocity 2.4 Distance–time graphs 2.5 Speed–time graphs 2.6 Acceleration 2.7 Free fall Key terms Worked examples Exam tips Experiments Quiz
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What you need to know

Cambridge IGCSE Physics 0625 · Syllabus 1.2 Motion. Tick each one when you can do it. Your ticks are saved on this device.

Core

  • 1Define speed as distance travelled per unit time; recall and use v = s / t.
  • 2Define velocity as speed in a given direction.
  • 3Recall and use average speed = total distance travelled ÷ total time taken.
  • 4Sketch, plot and interpret distance–time and speed–time graphs.
  • 5Tell from a graph or data when an object is at rest, moving at constant speed, accelerating or decelerating.
  • 6Calculate speed from the gradient of a straight part of a distance–time graph.
  • 7Calculate the distance travelled from the area under a speed–time graph (constant speed or constant acceleration).
  • 8State that the acceleration of free fall g near the Earth's surface is roughly constant, about 9.8 m/s2.

Extended (Supplement)

  • 9Define acceleration as change in velocity per unit time; recall and use a = Δv / Δt.
  • 10Tell from data or a speed–time graph when acceleration is constant or changing.
  • 11Calculate acceleration from the gradient of a speed–time graph.
  • 12Know that a deceleration is a negative acceleration and use this in calculations.
  • 13Describe objects falling with and without air or liquid resistance, including terminal velocity.

2.1Speed Core

How fast something moves, and how to calculate it.

Definition

Speed is the distance travelled per unit time, in other words how many metres an object moves each second.

v = st     speed = distancetime

Here v is the speed, s is the distance and t is the time. The SI unit of speed is the metre per second (m/s). You will also see km/h, for example on car speedometers.

t = 0 s t = 4.0 s distance travelled s = 100 m speed v = s ÷ t = 100 m ÷ 4.0 s = 25 m/s
Fig 2.1 Speed is the distance travelled in each second. This car travels 25 m every second.

Rearranging the equation

Exam questions often give you the speed and ask for the distance or the time. Use the triangle to rearrange:

s v t cover the one you want To find speed: v = s ÷ t To find distance: s = v × t To find time: t = s ÷ v s = distance (m) v = speed (m/s) t = time (s)
Fig 2.2 The speed triangle: cover the quantity you want and the triangle shows the calculation.

Changing units

Always check the units match before you calculate. If the distance is in km and the time in hours, the speed comes out in km/h. To get m/s, use metres and seconds.

km/h m/s ÷ 3.6 × 3.6 Why 3.6? 1 km/h = 1000 m ÷ 3600 s = 1 ÷ 3.6 m/s Example: 72 km/h ÷ 3.6 = 20 m/s · 15 m/s × 3.6 = 54 km/h
Fig 2.3 Converting between km/h and m/s.
Real life
  • Speed guns at cricket matches show fast bowlers reaching about 145 km/h. That is about 40 m/s, so the ball covers the 20 m pitch in about half a second.
  • Car speedometers show km/h. A car at 72 km/h covers 20 metres every second, which is why stopping distances are so long.
  • The fastest humans sprint at about 10 m/s; a cheetah can reach about 30 m/s.

2.2Average speed Core

Most journeys speed up, slow down and stop. Average speed describes the whole trip.

average speed = total distance travelledtotal time taken

A car's speed changes all the time in traffic. The average speed is the steady speed that would cover the same total distance in the same total time. Any time spent stopped still counts in the total time.

Home Bus stop School 2.4 km in 10 min stops 5 min 3.6 km in 15 min average speed = total distance ÷ total time = 6.0 km ÷ 30 min = 6.0 km ÷ 0.5 h = 12 km/h (the stop counts in the total time)
Fig 2.4 Average speed uses the whole journey, including stops.
Watch out

Don't average the speeds of different parts of a journey. If you drive 30 km at 60 km/h and then 30 km at 20 km/h, the average speed is not (60 + 20) ÷ 2 = 40 km/h. Total distance = 60 km, total time = 0.5 h + 1.5 h = 2 h, so the average speed is 30 km/h.

Real life
  • Map apps estimate your arrival time using an average speed for each road, including traffic lights and jams.
  • Some expressways use "average speed cameras": they record when your car passes two points a known distance apart and calculate distance ÷ time. Slowing down only near the cameras doesn't help!
  • Walking 1.2 km to school in 15 minutes is an average speed of 1.2 ÷ 0.25 = 4.8 km/h, even if you stopped to chat on the way.

2.3Velocity Core

Speed with a direction.

Definition

Velocity is speed in a given direction. Speed is a scalar; velocity is a vector.

Two cars moving at 20 m/s in opposite directions have the same speed but different velocities. Along a straight line we show direction with a sign: +20 m/s one way and −20 m/s the other. A car going round a roundabout at a steady speed has a changing velocity, because its direction keeps changing.

+20 m/s −20 m/s Same speed (20 m/s), different velocities because they move in opposite directions constant speed Speed stays the same, but velocity changes because the direction changes
Fig 2.5 Velocity is speed in a given direction.
Real life
  • A car on a roundabout at a steady 30 km/h is constantly changing velocity, because its direction keeps changing. That is why you feel pushed sideways.
  • The Earth moves around the Sun at about 30 km/s. Its speed is almost constant, but its velocity changes direction all the time.

2.4Distance–time graphs Core

Reading motion from a graph of distance against time.

A distance–time graph shows how far an object is from its starting point at each moment. The key idea is that the gradient (steepness) of the line equals the speed.

At rest t distance flat: distance not changingConstant speed t distance straight sloping lineAccelerating t distance curve gets steeperDecelerating t distance curve gets less steep
Fig 2.6 The four distance–time graph shapes you must recognise. The gradient (steepness) shows the speed.
  • Flat (horizontal) line: distance isn't changing, so the object is at rest (stationary).
  • Straight sloping line: equal distances in equal times, so constant speed.
  • Curve getting steeper: speed increasing, so accelerating.
  • Curve getting less steep: speed decreasing, so decelerating.
0 2 4 6 8 10 0 20 40 60 80 100 time / s distance / m A: 10 m/s B: 4 m/s steeper line = faster
Fig 2.7 On a distance–time graph, the steeper line is the faster object.

Speed from the gradient

For a straight-line section, draw a large right-angled triangle on the line and use:

speed = gradient = change in distancechange in time = ΔdΔt
0 2 4 6 8 10 0 10 20 30 40 50 time / s distance / m Δt = 8 − 2 = 6 s Δd = 40 − 10 = 30 m speed = gradient = 30 m ÷ 6 s = 5.0 m/s
Fig 2.8 Speed from the gradient of a distance–time graph. Use a large triangle for accuracy.

Reading a whole journey

Real journeys are made of several sections. Read each one separately: work out the gradient of each straight part, and spot any flat parts where the object stopped.

0 40 80 120 160 200 240 0 100 200 300 400 500 time / s distance from home / m A B CA walks: 150 m in 100 s speed = 1.5 m/sB stopped for 60 s speed = 0 (flat line)C runs: 300 m in 60 s speed = 5.0 m/s (steepest)Average speed overall= 450 m ÷ 220 s = 2.0 m/s
Fig 2.9 Reading a journey from a distance–time graph.

Ticker tape

In the lab, a ticker timer pulls paper tape behind a trolley and prints dots at equal time intervals (usually 50 per second). The spacing of the dots shows the motion.

equal spacing → constant speedspacing increases → acceleratingspacing decreases → deceleratingA ticker timer makes 50 dots per second, so each gap is 0.02 s.
Fig 2.10 Ticker tapes: the dots are made at equal time intervals, so the gaps show how far the trolley moved each time.
Real life
  • Delivery and taxi apps show your driver moving on a map. Behind the scenes, the app stores distance against time, so a stop at traffic lights is a flat section of the graph.
  • Fitness watches record distance and time on a run and plot your pace, which is the gradient of your distance–time graph.

2.5Speed–time graphs Core

Reading motion from a graph of speed against time, and finding the distance from the area.

A speed–time graph shows the speed at each moment. It looks similar to a distance–time graph, but it means something different, so always read the axis labels first.

At rest t speed line along the time axisConstant speed t speed flat (horizontal) lineAccelerating t speed line slopes upwardsDecelerating t speed line slopes downwards
Fig 2.11 The same four motions on speed–time graphs. Careful: a flat line now means constant speed, not at rest.
  • Line along the time axis: speed is zero, so the object is at rest.
  • Flat line above the axis: speed not changing, so constant speed.
  • Line sloping up: speed increasing, so accelerating. A straight slope means constant acceleration.
  • Line sloping down: speed decreasing, so decelerating.
time distance time speed distance–timespeed–timeBoth graphs show the SAME motion: moving at a constant speed.
Fig 2.14 Always check the axis label first. A sloping line on a distance–time graph and a flat line on a speed–time graph mean the same thing.

Changing acceleration Extended

A straight sloping line means constant acceleration. A curved line means the acceleration is changing: getting steeper means the acceleration is increasing, and flattening off means it is decreasing.

time speed acceleration increasing (curve gets steeper) time speed acceleration decreasing (curve gets flatter)
Fig 2.12 A curved speed–time graph means the acceleration is changing.

Distance from the area under the graph

The area under a speed–time graph equals the distance travelled. For constant speed or constant acceleration, split the area into rectangles and triangles:

  • Rectangle: area = base × height
  • Triangle: area = ½ × base × height
0 2 4 6 8 10 0 3 6 9 12 15 time / s speed / m/s triangle ½ × 4 × 12 = 24 m rectangle 6 × 12 = 72 mdistance = area under the graph = 24 + 72 = 96 m
Fig 2.13 The area under a speed–time graph is the distance travelled. Split the shape into triangles and rectangles.
Units check

Area = (time in s) × (speed in m/s) = metres. If the time axis is in minutes or hours, convert first or the answer will be wrong.

Real life
  • A metro train between two stations makes a classic speed–time graph: it accelerates out of the station, cruises at constant speed, then decelerates to stop at the next platform. The area under the graph is the distance between the stations.
  • Aircraft "black box" flight recorders log speed against time, which investigators use to rebuild a flight.

2.6Acceleration Extended

How quickly the velocity changes.

Definition

Acceleration is the change in velocity per unit time.

a = ΔvΔt = final velocity − initial velocitytime taken

The unit is metres per second squared (m/s2). An acceleration of 4 m/s2 means the velocity goes up by 4 m/s every second.

t = 0 s0 m/st = 1 s4 m/st = 2 s8 m/st = 3 s12 m/s+4 m/s+4 m/s+4 m/sThe velocity increases by 4 m/s every second, so the acceleration is 4 m/s².
Fig 2.15 Acceleration is how much the velocity changes each second.

Acceleration from a speed–time graph

The gradient of a speed–time graph equals the acceleration.

0 2 4 6 8 0 8 16 24 time / s speed / m/s Δt = 8 s Δv = 16 m/s 0 2 4 6 0 10 20 30 time / s speed / m/s Δv = −30 m/s Δt = 6 sa = 16 ÷ 8 = 2.0 m/s²a = −30 ÷ 6 = −5.0 m/s²(a deceleration of 5.0 m/s²)
Fig 2.16 Acceleration is the gradient of a speed–time graph. A downward slope gives a negative acceleration (a deceleration).
Deceleration

A deceleration is a negative acceleration: the object is slowing down. If a car's acceleration is −5.0 m/s2, we can also say it decelerates at 5.0 m/s2. In calculations, final velocity − initial velocity comes out negative.

Real life
  • Car adverts quote "0–100 km/h in 8 seconds". 100 km/h ≈ 28 m/s, so the average acceleration is about 28 ÷ 8 ≈ 3.5 m/s².
  • An aircraft on take-off accelerates at about 2–3 m/s², pressing you back into your seat.
  • Airbags and crumple zones make a crash last longer, so the deceleration of the passengers is smaller.

2.7Free fall & terminal velocity Core

What happens when things fall.

An object falling with no air resistance is in free fall. Near the Earth's surface, all objects in free fall have the same, roughly constant acceleration, the acceleration of free fall, g:

g ≈ 9.8 m/s2

So a falling object's speed increases by about 9.8 m/s every second, whatever its mass. A heavy ball and a light ball dropped together in a vacuum land at the same time.

Ball falling (no air resistance)0.0 s0.2 s0.3 s0.4 s0.5 sequal time intervals,gaps get bigger 0 1 2 3 4 0 10 20 30 40 time / s speed / m/s 9.8 19.6 29.4 gradient = g = 9.8 m/s²
Fig 2.17 In free fall the speed rises by about 9.8 m/s every second: the acceleration of free fall, g.

Falling through air or liquid Extended

In real life, air (or a liquid) pushes against a falling object. This air resistance (drag) gets bigger as the object goes faster.

  1. At first the object is slow, so air resistance is small. The weight is much bigger, so it accelerates at about 9.8 m/s2.
  2. As it speeds up, air resistance grows. The resultant force gets smaller, so the acceleration decreases.
  3. Eventually air resistance equals the weight. The forces are balanced, the resultant force is zero, and the object falls at a steady top speed: its terminal velocity.
0 2 4 6 8 10 0 20 40 60 time / s speed / m/s no air resistance (straight line, gradient 9.8) with air resistance: levels off at terminal velocity
Fig 2.18 Air resistance makes the acceleration fall until the object reaches terminal velocity.
Just jumpedW > air resistancespeeds upFalling fasterW > air resistancespeeds up lessTerminal velocityW = air resistanceconstant speedParachute opensair resistance > Wslows downWair resistance
Fig 2.19 Forces on a skydiver. Blue: weight (W, constant). Red: air resistance, which grows as the skydiver speeds up.

When a skydiver opens a parachute, air resistance suddenly becomes much bigger than the weight, so they decelerate. As they slow down, air resistance drops until it equals the weight again, giving a new, much lower terminal velocity that is safe for landing.

0 10 20 30 40 50 60 0 20 40 60 time / s speed / m/s A B C D EA accelerating: weight > air resistanceB terminal velocity: forces balancedC parachute opens: big decelerationD new, lower terminal velocityE lands
Fig 2.20 Speed–time graph for a skydiver, with the two terminal velocities.

The same happens to a ball bearing dropped into a tall tube of oil. Because oil resists motion much more than air, the ball reaches its terminal velocity quickly and then falls at a steady speed.

Try it in the 3D lab

You can find g from a pendulum in our Simple Pendulum simulator. Simulators for average speed, ticker tape and free fall are coming soon.

Real life
  • Raindrops fall from clouds hundreds of metres up, but they don't hurt you. Air resistance gives them a terminal velocity of only a few metres per second (up to about 9 m/s for big drops).
  • Skydivers spread out flat to increase air resistance and fall more slowly, then dive head-first to go faster.
  • On the Moon there is no air, so a hammer and a feather dropped together land at the same time. Astronauts showed this on the Apollo 15 mission.

Key terms & formulae

Learn these word for word. Definitions earn easy marks.

SpeedDistance travelled per unit time. Unit: m/s.
Average speedTotal distance travelled ÷ total time taken.
VelocitySpeed in a given direction (a vector).
Gradient of a distance–time graphEquals the speed.
Area under a speed–time graphEquals the distance travelled.
Acceleration of free fall, gAbout 9.8 m/s² near the Earth's surface, roughly constant.
Acceleration ExtChange in velocity per unit time. Unit: m/s².
Deceleration ExtA negative acceleration: the object is slowing down.
Gradient of a speed–time graph ExtEquals the acceleration.
Terminal velocity ExtThe constant top speed of a falling object, reached when air resistance equals its weight.

Formulae

v = s ÷ t
Speed = distance ÷ time
average speed = total distance ÷ total time
Whole journey, stops included
km/h ÷ 3.6 = m/s
and m/s × 3.6 = km/h
speed = Δd ÷ Δt
Gradient of a distance–time graph
distance = area under graph
Speed–time graph: rectangles + triangles (½ × b × h)
a = Δv ÷ Δt
Acceleration; also the gradient of a speed–time graph Ext

Worked examples

Try each one yourself first, then open the solution.

1A car travels 150 m in 6.0 s at a steady speed. Calculate its speed. Coresolution
Equationv = s ÷ t
Workingv = 150 ÷ 6.0 = 25 m/s
Speed = 25 m/s
2A cyclist rides at 8.0 m/s for 45 s. How far does she travel? Coresolution
Rearranges = v × t
Workings = 8.0 × 45 = 360 m
Distance = 360 m
3A train travels 12 km in 10 minutes, stops at a station for 5 minutes, then travels 18 km in 15 minutes. Find its average speed in km/h and in m/s. Coresolution
Totalsdistance = 12 + 18 = 30 km; time = 10 + 5 + 15 = 30 min = 0.50 h (the stop counts)
Workingaverage speed = 30 ÷ 0.50 = 60 km/h
Convert60 ÷ 3.6 = 16.7 m/s ≈ 17 m/s
60 km/h ≈ 17 m/s
4A speed–time graph shows a car accelerating steadily from rest to 12 m/s in 4.0 s, then moving at 12 m/s for another 6.0 s. How far does it travel in the 10 s? Coresolution
IdeaDistance = area under the graph: a triangle then a rectangle (see Fig 2.13).
Triangle½ × 4.0 × 12 = 24 m
Rectangle6.0 × 12 = 72 m
Distance = 24 + 72 = 96 m
5A bus speeds up from 4.0 m/s to 20 m/s in 8.0 s. Calculate its acceleration. Extendedsolution
Equationa = Δv ÷ Δt
Workinga = (20 − 4.0) ÷ 8.0 = 16 ÷ 8.0 = 2.0 m/s2
Acceleration = 2.0 m/s2
6A car travelling at 30 m/s brakes and stops in 6.0 s. Calculate its acceleration and the distance it travels while braking. Extendedsolution
Accelerationa = (0 − 30) ÷ 6.0 = −5.0 m/s2 (a deceleration of 5.0 m/s2)
DistanceArea of the triangle under the speed–time graph = ½ × 6.0 × 30 = 90 m
a = −5.0 m/s2; distance = 90 m

Exam tips & common mistakes

Where students most often lose marks on this topic.

Common mistakes
  • Mixing up the two graphs. A flat line means at rest on a distance–time graph but constant speed on a speed–time graph. Read the axes first.
  • Averaging the speeds of different parts of a journey instead of using total distance ÷ total time.
  • Leaving out time spent stopped when finding average speed.
  • Mixing units: km with seconds, or minutes with m/s. Convert first.
  • Forgetting the ½ when finding the area of a triangle under a speed–time graph.
  • Writing the acceleration as (initial − final) instead of (final − initial) ÷ time. A slowing object must give a negative answer.
  • Saying a skydiver at terminal velocity has "no forces" acting. The forces are balanced: weight = air resistance, so the resultant force is zero.
Graph skills
  • Draw a large gradient triangle (more than half the line) and show the readings you used.
  • When describing a graph, describe each section in order: "accelerates, then constant speed, then decelerates to rest".
  • When sketching, label both axes with quantity and unit, and start at the origin if the object starts from rest.
Words examiners look for
  • Speed: "distance travelled per unit time".
  • Velocity: "speed in a given direction".
  • Acceleration: "change in velocity per unit time".
  • Terminal velocity: "air resistance equals weight, so the resultant force is zero and the speed is constant".

Try it in the 3D lab

The IGCSE practicals for this chapter. Ready simulators open straight away.

Chapter 2 quiz

10 exam-style multiple-choice questions. Choose an answer for each, then check your score.