Home › Learning Hub › IGCSE Physics › 1a Measurement and motion
Topic 1 · 1.1–1.2

Measurement and motion

Core and Extended · Papers 1–6

🎯What you need to be able to do

  • Use rulers, measuring cylinders, clocks and digital timers; find a small distance or a short time by measuring multiples.
  • Tell scalars from vectors; find the resultant of two vectors at right angles EXTENDED.
  • Use \( v = \dfrac{s}{t} \) and average speed; sketch, plot and interpret distance–time and speed–time graphs.
  • Find speed from a gradient and distance from an area; use \( a = \dfrac{\Delta v}{\Delta t} \), deceleration and changing acceleration EXTENDED.
  • State that \( g \approx 9.8 \) m/s2; describe falling with and without air resistance, and terminal velocity EXTENDED.

📚The physics

Measuring length, volume and time

A ruler measures length to the nearest millimetre. Read it with your eye directly above the mark to avoid parallax, and check where the object starts — it need not be at zero. A measuring cylinder measures the volume of a liquid: read the bottom of the meniscus with your eye level with it.

Left: a pencil on a centimetre ruler, starting at 1.0 cm and ending at 8.3 cm, so its length is 7.3 cm. An eye directly above the end of the pencil reads correctly; an eye at an angle gives a parallax error. Right: a measuring cylinder containing water, with the eye level with the bottom of the curved meniscus, reading 34 cubic centimetres.
Subtract the starting reading; read the bottom of the meniscus at eye level.

Time intervals are measured with a stop-watch or digital timer (light gates for very short times). Your reaction time is about 0.2 s, so short times and small distances are found by measuring multiples: time 20 swings of a pendulum and divide by 20; measure the thickness of 100 sheets of paper and divide by 100.

A pendulum swinging between A and B, with a fiducial mark below its lowest point. One oscillation is from A to B and back to A. A box explains that 20 oscillations took 28.4 s, so the period is 28.4 divided by 20, which is 1.42 s, because reaction time is shared over 20 swings.
The period is the time for one complete oscillation.

Scalars and vectors EXTENDED

A scalar has magnitude (size) only; a vector has magnitude and direction.

scalars: distance, speed, time, mass, energy, temperature
vectors: force, weight, velocity, acceleration, momentum, electric field strength, gravitational field strength

Two vectors at right angles combine to a resultant found by Pythagoras (or a scale drawing), with the direction from trigonometry.

A plane flies at 120 metres per second north while the wind blows at 50 metres per second east. Drawn tip to tail, the resultant is 130 metres per second at 23 degrees east of north.
EXTENDED Draw the vectors tip to tail; the resultant joins the start to the end.

Speed, velocity and acceleration

\[ v = \frac{s}{t} \qquad \text{average speed} = \frac{\text{total distance travelled}}{\text{total time taken}} \]

Speed is distance travelled per unit time; velocity is speed in a given direction. EXTENDED Acceleration is change in velocity per unit time, \( a = \dfrac{\Delta v}{\Delta t} \), in m/s2. A deceleration is a negative acceleration.

Motion graphs

Four distance-time graphs. At rest: a horizontal line. Constant speed: a straight sloping line. Accelerating: a curve getting steeper. Decelerating: a curve getting less steep.
On a distance–time graph, the gradient is the speed.
  • Distance–time graph: gradient = speed. Horizontal = at rest; straight slope = constant speed.
  • Speed–time graph: horizontal = constant speed; straight slope = constant acceleration; EXTENDED a curve means changing acceleration, and the gradient = acceleration.
  • The area under a speed–time graph = distance travelled.

Falling objects

Near the Earth’s surface, the acceleration of free fall g is approximately constant, about 9.8 m/s2. EXTENDED Without air resistance, every object falls with this acceleration. With air resistance, the drag grows as the object speeds up, so the resultant force and the acceleration fall until drag equals weight: the object then falls at a constant terminal velocity.

A speed-time graph for a skydiver. The speed rises steeply at first, following the no-air-resistance line, then the curve becomes less steep and levels off at a terminal velocity of about 55 metres per second. Force diagrams: at the start only weight acts; while speeding up, weight is larger than air resistance; at terminal velocity the two are equal.
EXTENDED Terminal velocity: weight and air resistance are balanced, so the acceleration is zero.

✏️Worked example

A bus pulls away from a stop, travels at a steady speed, then brakes to rest at the next stop. (a) Describe the motion in each of the three stages. [3] (b) Calculate the total distance travelled. [3] (c) EXTENDED Calculate the acceleration in the first 8 s and the deceleration at the end. [3] (d) Calculate the average speed for the whole journey. [2]
A speed-time graph: the speed rises steadily from 0 to 12 metres per second in 8 seconds, stays at 12 metres per second until 28 seconds, then falls steadily to 0 at 34 seconds. The areas are marked 48 m, 240 m and 36 m, making 324 m.

(a) 0–8 s: constant acceleration; 8–28 s: constant speed of 12 m/s; 28–34 s: constant deceleration.

(b) Area under the graph: \( \tfrac12 \times 8 \times 12 + 20 \times 12 + \tfrac12 \times 6 \times 12 = 48 + 240 + 36 = 324 \) m.

(c) \( a = \dfrac{12 - 0}{8} = 1.5 \) m/s2; at the end \( a = \dfrac{0 - 12}{6} = -2.0 \) m/s2, a deceleration of 2.0 m/s2.

(d) \( \dfrac{324}{34} = 9.5 \) m/s.

Check it. The average speed must lie between 0 and the top speed of 12 m/s — and closer to 12, because most of the time is spent at 12 m/s.
Reading the wrong graph. On a speed–time graph a horizontal line is constant speed, not “stopped”. Always read the y-axis label first.

📝Practise

In the style of the multiple-choice, theory and practical papers. EXTENDED marks Supplement content.

1. (Multiple choice.) Which list contains only vector quantities? A: force, mass, velocity. B: momentum, weight, acceleration. C: speed, energy, weight. D: time, distance, temperature.
B. Mass, speed, energy, time, distance and temperature are scalars.
2. (Theory.) A runner completes 1500 m in 4.0 minutes. Calculate her average speed in m/s. [2] (Modelled on 0625/32 June 2026 Q1(b).)
Time = 4.0 × 60 = 240 s; average speed = 1500 / 240 = 6.3 m/s (6.25). Converting minutes to seconds is the mark most often lost.
3. (Practical.) Describe how to find the thickness of one sheet of paper using a 30 cm ruler. [2]
Measure the thickness of a stack of many sheets (e.g. 200) with the ruler, then divide by the number of sheets. A single sheet is far thinner than the 1 mm resolution of the ruler.
A speed-time graph for a cyclist: from A at the origin the speed rises in a straight line to B, 9 metres per second at 6 seconds; it stays at 9 metres per second until C at 15 seconds; then it falls along a curve that becomes less steep, reaching zero at D, 25 seconds.
For questions 4 and 5.
4. (Theory.) The graph shows a cyclist’s journey. State the motion between A and B, B and C, and C and D. [3] (Modelled on 0625/42 June 2026 Q1(a).)
A–B: constant acceleration. B–C: constant speed (9 m/s). C–D: decelerating, with a decreasing deceleration (the gradient gets less steep).
5. (Theory.) Using the graph, calculate the distance travelled in the first 15 s, and EXTENDED the acceleration between A and B. [4]
Area = \( \tfrac12 \times 6 \times 9 + 9 \times 9 = 27 + 81 = \) 108 m. Acceleration = \( \dfrac{9}{6} = \) 1.5 m/s2.
6. (Theory.) EXTENDED A boat heads east at 4.0 m/s across a river flowing south at 3.0 m/s. Calculate the magnitude of its resultant velocity. [2]
\( \sqrt{4.0^2 + 3.0^2} = \sqrt{25} = \) 5.0 m/s (at 37° south of east).
7. (Theory.) EXTENDED A skydiver jumps from a plane. Explain, in terms of forces, why her speed increases at first but then becomes constant. [3]
At first the weight is greater than air resistance, so there is a resultant downward force and she accelerates. As speed increases, air resistance increases, so the resultant force (and acceleration) decreases. When air resistance equals weight the resultant force is zero: she moves at constant (terminal) velocity.
8. (Theory.) EXTENDED A car travelling at 25 m/s brakes to rest in 5.0 s. Calculate its deceleration. [2]
\( a = \dfrac{0 - 25}{5.0} = -5.0 \) m/s2, a deceleration of 5.0 m/s2.

🔗Go deeper — other people’s work

These are external resources, not mine. If one stops working, tell me and everything above it on this page still stands.

  • PhET “The Moving Man” — position, velocity and acceleration graphs in real time
  • The Physics Classroom — describing motion with graphs