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IGCSE Physics 0625 · Chapter 1 notes · ~10 min read

Measurement & motion

How to measure properly, then the whole story of speed, acceleration and motion graphs — the topic that decorates every Paper 2 and Paper 4.

Measuring instrumentsScalars & vectorsSpeed & velocityAccelerationDistance–time & speed–time graphsFree fall & terminal velocity
RSby Riyaz Sir
mentorriyaz.in
No tag = Core (everyone)EXTENDED Extended onlyhighlight = comes up again and againTest yourself at the end

In 30 seconds

  • Every measurement needs a number AND a unit. Read instruments at eye level and measure many to reduce error.
  • Speed = distance ÷ time. Acceleration = change in speed ÷ time.
  • Distance–time graph: gradient = speed. Speed–time graph: gradient = acceleration, area = distance.
  • EXT A falling object speeds up until air resistance = weight, then moves at terminal velocity.

By the end you can

  • Read a ruler, measuring cylinder and stopwatch correctly, and spread the error by measuring many.
  • Tell scalars from vectors and add two perpendicular vectors. EXT
  • Use v = s ÷ t and a = Δv ÷ Δt, including unit conversions.
  • Sketch and read distance–time and speed–time graphs, and find distance from an area.
  • Explain terminal velocity step by step, with forces. EXT

1Measuring things

Quantities and SI units

QuantitySI unitMeasured with
lengthmetre (m)ruler, tape measure
masskilogram (kg)balance
timesecond (s)stopwatch, digital timer
volumem³ (also cm³, litre)measuring cylinder; displacement for solids

Prefixes and conversions

PrefixMeaningExample
kilo (k)× 10001 km = 1000 m
centi (c)÷ 1001 m = 100 cm
milli (m)÷ 10001 m = 1000 mm
micro (µ)÷ 1 000 0001 m = 1 000 000 µm
mega (M)× 1 000 0001 MHz = 10⁶ Hz
  • 1 cm³ = 1 mL and 1 litre = 1000 cm³. Time: 1 h = 3600 s.

Read the measuring cylinder properly

10 mL20 mL30 mL40 mL50 mL60 mLeye level ✓too high ✗read the bottomof the meniscus
Eye level with the liquid, and read the BOTTOM of the meniscus (the curved surface). Reading from above gives a false value (parallax error).
Common mistakeReading the top of the meniscus, or the scale from above or below.

Measure many, then divide

Picture itOne sheet of paper is far too thin to measure, but 200 sheets make a stack you can measure easily. The tiny error in your ruler is shared out over 200 sheets — so it matters 200 times less.
  • Thickness of one sheet = thickness of a stack ÷ number of sheets.
  • Period of a pendulum = time for many swings ÷ number of swings. This also shrinks the effect of your slow reaction time (about 0.2 s).
ABone swing: A → B → A (T = time for ONE swing)
One swing = A to B and back to A. Time 20 swings and divide by 20.
Worked example

A stack of 200 sheets of paper is 2.0 cm thick. What is the thickness of one sheet?

  1. 2.0 cm = 20 mm
  2. 20 mm ÷ 200
  3. = 0.10 mm
Worked example

20 swings of a pendulum take 32 s. What is the period T?

  1. T = total time ÷ number of swings
  2. T = 32 ÷ 20
  3. = 1.6 s

2Scalars and vectors

Scalars and vectorsEXTENDED

Scalar — has size (magnitude) only. Examples: distance, speed, time, mass, energy, temperature.

Vector — has size AND direction. Examples: displacement, velocity, acceleration, force, weight, momentum, field strength.

Picture it"5 km" is a scalar — it only tells you how far you walked. "5 km north" is a vector — it also tells you where you ended up.
  • Forces on the same line: add if they point the same way, subtract if they point opposite ways.
  • Two vectors at a right angle: draw them head-to-tail; the resultant is the diagonal, so use Pythagoras (and tan θ for the direction).
θeast 3 m/snorth 4 m/sR = 5 m/sR² = 3² + 4² → R = 5
A boat pointing east at 3 m/s in a river flowing north at 4 m/s actually moves at 5 m/s, in a direction 53° north of east.
Worked example

A boat heads east at 3 m/s. The river flows north at 4 m/s. Find the resultant speed and direction.

  1. Draw the vectors head-to-tail at a right angle
  2. R² = 3² + 4² = 25
  3. R = 5 m/s
  4. tan θ = 4 ÷ 3, so θ = 53° north of east

3Speed, velocity and acceleration

Speed and velocity

v = st
speed (m/s) = distance (m) ÷ time (s)
average speed = total distancetotal time
includes stops — use ALL the time

Velocity — speed in a stated direction (a vector). Going round a bend at constant speed still changes your velocity, because the direction changes.

  • To convert: km/h → m/s: ÷ 3.6. m/s → km/h: × 3.6. (72 km/h = 20 m/s.)
Worked example

A cyclist rides 3.0 km in 10 minutes. Find the average speed in m/s and km/h.

  1. Convert first: 3.0 km = 3000 m, 10 min = 600 s
  2. v = 3000 ÷ 600 = 5.0 m/s
  3. × 3.6 = 18 km/h
Common mistakeMixing units (km with seconds). Convert before you divide.

AccelerationEXTENDED

a = ΔvΔt = final speed − initial speedtime taken
unit m/s² (metres per second, every second)
  • Deceleration is a negative acceleration (slowing down).
  • Constant acceleration → a straight sloping line on a speed–time graph. A curve means the acceleration is changing.
Picture itA car with a = 2 m/s² gains 2 m/s of speed every second: 0, 2, 4, 6, 8 m/s …
Worked example

A car speeds up from 4 m/s to 20 m/s in 8 s. Find its acceleration.

  1. Change in speed: Δv = 20 − 4 = 16 m/s
  2. a = Δv ÷ Δt = 16 ÷ 8
  3. = 2 m/s²

4Motion graphs

Distance–time graph

time / sdistance / mABCDA steady speed · B at rest · C faster · D returninggradient = speed, so a flat line = not moving
Steeper line = faster. A flat line = at rest. A line coming back down means the object is returning.
  • Gradient = speed. Straight line = constant speed. A curve that steepens = speeding up.
  • Horizontal line = stationary (distance not changing).
Common mistakeReading a flat line on a distance–time graph as "constant speed". It means the object has stopped.

Speed–time graph

time / sspeed / m/s41014816 m48 m16 mgradient = accelerationarea under graph = distance (16 + 48 + 16 = 80 m)
Gradient = acceleration. Area under the graph = distance travelled.
  • Horizontal line = constant speed (NOT at rest — rest is the line along the x-axis).
  • Sloping up = accelerating; sloping down = decelerating. Area under the line = distance.
  • Split the area into triangles (½ × base × height) and rectangles (base × height).
Exam tipIn "find the distance" questions, quote the units and show the shapes you added: 16 + 48 + 16 = 80 m.
Worked example

Use the graph above: find (a) the acceleration during the first 4 s and (b) the distance travelled in total.

  1. (a) a = gradient = 8 ÷ 4 = 2 m/s²
  2. (b) Triangle 1: ½ × 4 × 8 = 16 m
  3. Rectangle: 6 × 8 = 48 m
  4. Triangle 2: ½ × 4 × 8 = 16 m
  5. Total distance = 80 m

5Falling objects

Free fall

  • Near the Earth's surface, a falling object with no air resistance accelerates at g = 9.8 m/s² (the same for heavy and light objects).
  • That means its speed rises by about 9.8 m/s every second: 0 → 9.8 → 19.6 → 29.4 m/s …
  • With air resistance the acceleration is smaller — a feather falls slower than a stone in air, but they fall together in a vacuum.

Terminal velocityEXTENDED

1 just jumpedresultant ↓ large2 speeding upresultant ↓ smaller3 terminal velocityresultant = 0red = air resistance (grows with speed) blue = weight (stays 600 N)
Weight stays the same. Air resistance grows as speed grows, until the two forces are equal.
  • 1. At the start air resistance is tiny, so weight is bigger: big resultant force down, big acceleration.
  • 2. As speed rises, air resistance rises, so the resultant force (and acceleration) gets smaller.
  • 3. When air resistance = weight, the resultant force is zero, so the speed stays constant: terminal velocity.
timespeedterminal velocityparachute opensnew, lower terminal velocityspeed rises → drag rises → forces balance → constant speed
A parachute opens: air resistance jumps above weight, so the skydiver slows down to a new, lower terminal velocity.
Exam tipNever say "gravity stops". Gravity (weight) is still there — the forces are BALANCED, so there is no acceleration.
Common mistakeSaying the speed is zero at terminal velocity. The speed is constant and not zero.

6Test yourself

Test yourself — cover the answers first

Quick check

  1. Convert 90 km/h into m/s.
  2. 20 swings of a pendulum take 30 s. Find the period.
  3. What does a horizontal line mean on (a) a distance–time graph and (b) a speed–time graph?
  4. What does the area under a speed–time graph represent?
  5. Is velocity a scalar or a vector? Why?
  6. Name the instrument and the correct way to read the volume of a liquid.

Exam-style

  1. A cyclist accelerates uniformly from rest to 12 m/s in 6.0 s, then rides at constant speed for 20 s. Calculate (a) the acceleration, (b) the total distance.
  2. Two forces act on an object: 6.0 N east and 8.0 N north. Find the size of the resultant force.
  3. A skydiver reaches terminal velocity. Explain this in terms of forces. [3]
  4. A car travels 120 km in 1.5 h, stops for 30 min, then travels 60 km in 1.0 h. Calculate its average speed for the whole journey.
Show answers
  1. 90 ÷ 3.6 = 25 m/s
  2. 30 ÷ 20 = 1.5 s
  3. (a) stationary (b) constant speed
  4. the distance travelled
  5. A vector — it has direction as well as size.
  6. A measuring cylinder; eye level with the liquid, reading the bottom of the meniscus.
  7. (a) a = Δv ÷ Δt = 12 ÷ 6.0 = 2.0 m/s²
    (b) first 6 s: ½ × 6.0 × 12 = 36 m
    next 20 s: 12 × 20 = 240 m
    total = 276 m
  8. R² = 6.0² + 8.0² = 100
    R = 10 N
  9. Air resistance increases as the speed increases
    until air resistance equals the weight
    the resultant force is then zero, so the acceleration is zero and the speed is constant
  10. total distance = 120 + 60 = 180 km
    total time = 1.5 + 0.5 + 1.0 = 3.0 h
    average speed = 180 ÷ 3.0 = 60 km/h
Practise this chapter
MotionMeasurementPendulums & timing
Next chapterMass, weight & density →
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