Sketch, plot and interpret distance-time and speed-time graphs

Cambridge IGCSE Physics 0625 – Motion (Core + Supplement)

Objective

Students will be able to measure, sketch, plot and interpret distance‑time, speed‑time and (where required) velocity‑time graphs, and to relate these graphs to the underlying physical quantities of motion. They will also develop a working knowledge of the related core topics – density, pressure, thermal physics, waves, electricity & magnetism – as required by the 2026‑2028 Cambridge IGCSE Physics syllabus.

1 . Measuring Motion

• Ruler / measuring tape – gives distance travelled (m or cm).
• Stopwatch or digital timer – records elapsed time (s).
• For repeated trials record each (t, s) pair and calculate the average speed:

  \$\bar v=\frac{\displaystyle\sum{i=1}^{n}si}{\displaystyle\sum{i=1}^{n}ti}\$

• The gradient of a straight‑line portion of a distance‑time graph gives the same average speed.

2 . Key Concepts (Scalar & Vector)

3 . Density & Pressure (Core 1.4, 1.8)

• Density tells why some objects float while others sink. Example: steel has ρ ≈ 7 800 kg m⁻³, water ρ ≈ 1 000 kg m⁻³ → a steel ship floats because its overall (average) density, including air inside, is less than that of water.
• Pressure is crucial for fluids and gases. Example: a tyre supports a 600 N load because the contact area is only 0.02 m², giving a pressure of 30 kPa.

4 . Thermal Physics (Core 2.1‑2.3)

• Kinetic particle model – matter consists of particles in constant motion; temperature measures the average kinetic energy.
• Specific heat capacity (c) – amount of heat required to raise 1 kg of a substance by 1 K: Q = mcΔT.
• Heat transfer methods:

  • Conduction – direct particle collisions (e.g., metal rod).
  • Convection – bulk movement of fluid (e.g., heated air rising).
  • Radiation – emission of electromagnetic waves (e.g., Sun).

• Practical example – measuring the specific heat of water using a calorimeter: heat a known mass of water, record temperature change, apply Q = mcΔT.

5 . Waves (Core 3.1‑3.2)

• Wave definition – a disturbance that transfers energy without permanent displacement of the medium.
• Types:

  • Transverse – particle motion ⟂ to direction of travel (e.g., water surface ripples).
  • Longitudinal – particle motion ‖ to direction of travel (e.g., sound).

• – v = fλ, where f is frequency and λ wavelength.
• Reflection, refraction & diffraction – basic behaviours observable with a ripple tank or a simple sound‑tube experiment.

6 . Electricity & Magnetism (Core 4.1‑4.5)

• Charge (q) – property of particles; measured in coulombs (C). Like charges repel, unlike attract.
• Current (I) – flow of charge, I = Δq/Δt (A).
• Resistance (R) – opposition to current, V = IR (Ω).
• Potential difference (V) – energy per unit charge, measured in volts (V).
• Simple circuit diagram – battery, resistor, switch, and ammeter; students should be able to label and interpret.
• Electromagnetism – a current‑carrying conductor produces a magnetic field; the right‑hand rule predicts direction.

7 . Sketching Distance‑Time Graphs

A distance‑time graph shows how far an object has moved from a fixed origin as a function of time.

• Axes: horizontal – time (t, s); vertical – distance (s, m).
• Horizontal line → object at rest (gradient = 0).
• Straight line with constant positive gradient → uniform speed; speed = gradient (Δs/Δt).
• Curved line → speed changing (acceleration or deceleration); instantaneous speed = local gradient.

8 . Sketching Speed‑Time Graphs

A speed‑time graph displays the magnitude of the object's speed versus time.

• Axes: horizontal – time (t, s); vertical – speed (v, m s⁻¹).
• Line on the time axis → object at rest.
• Horizontal line above the axis → constant speed.
• Straight line with positive gradient → uniform (constant) acceleration; acceleration = gradient (Δv/Δt).
• Straight line with negative gradient → uniform deceleration.
• Area under the curve (between the line and the time axis) gives the distance travelled:

  \$\text{distance}= \int v\,dt\$

  For straight‑line sections, use simple geometric shapes (rectangle, triangle, trapezium).

9 . Sketching Velocity‑Time Graphs (Extended Content)

Velocity‑time graphs are optional for the core syllabus but essential for the supplement.

• Vertical axis shows signed speed (positive = chosen direction, negative = opposite direction).
• Gradient = acceleration (as for speed‑time graphs).
• Signed area under the line = displacement (not just distance).

10 . Plotting Real Data

1. Label each axis with the quantity and its unit.
2. Choose scales that make the data fill most of the graph area without crowding.
3. Plot each measured (t, s) or (t, v) pair as a small, clearly visible point.
4. Connect points with a smooth curve; use a straight ruler only for sections known to be uniform.
5. Draw a best‑fit straight line through any uniform‑motion region and note its gradient.

11 . Interpreting Graphs

12 . Sample Calculations

12.1 Constant speed

Object moves at 4 m s⁻¹ for 5 s.

\$\text{distance}=v\times t = 4\;\text{m s}^{-1}\times5\;\text{s}=20\;\text{m}\$

12.2 Acceleration from a speed‑time graph

Line from (0 s, 0 m s⁻¹) to (3 s, 9 m s⁻¹).

\$a=\frac{\Delta v}{\Delta t}= \frac{9-0}{3-0}=3\;\text{m s}^{-2}\$

12.3 Distance from the same graph (area)

Right‑angled triangle:

\$\text{distance}= \frac12 \times \text{base} \times \text{height}= \frac12 \times3\;\text{s}\times9\;\text{m s}^{-1}=13.5\;\text{m}\$

12.4 Uniform acceleration (worked example)

Car accelerates from rest to 12 m s⁻¹ in 4 s.

• Acceleration: \$a=\frac{12-0}{4}=3\;\text{m s}^{-2}\$
• Distance during acceleration (triangle area): \$s=\frac12\times4\;\text{s}\times12\;\text{m s}^{-1}=24\;\text{m}\$

12.5 Momentum & Impulse

A 2 kg ball is struck by a force of 10 N for 0.5 s.

• Impulse: \$F\Delta t = 10\times0.5 = 5\;\text{N s}\$
• Change in momentum: \$\Delta p = 5\;\text{kg m s}^{-1}\$
• If the ball was initially at rest, final speed \$v = \Delta p/m = 5/2 = 2.5\;\text{m s}^{-1}\$

13 . Forces, Newton’s First Law & Friction (Core 1.5)

• Motion changes only when a net external force acts (Newton’s 1st Law).
• Resultant force and acceleration: \$F = ma\$.
• Friction – resistive force opposing motion.

  • Kinetic friction: \$fk = \muk N\$.
  • Static friction: \$fs \le \mus N\$ (prevents motion until a threshold).

• Torque (moment of force) – tendency of a force to cause rotation: \$\tau = F\,d\$ (where \$d\$ is the perpendicular distance from the line of action to the pivot).

14 . Momentum & Impulse (Supplement 1.6)

• Momentum: \$p = mv\$ (vector).
• Impulse–momentum theorem: \$F\Delta t = \Delta p = m\Delta v\$.
• Conservation of momentum applies when the net external impulse on a system is zero (e.g., collisions).

15 . Energy, Work & Power (Core 1.7 + Supplement)

Graph connections:

• Area under a force‑time graph = impulse.
• Area under a power‑time graph = energy transferred.

16 . Common Misconceptions

• Confusing the slope of a speed‑time graph (acceleration) with the area under it (distance).
• Assuming a curved distance‑time graph always means deceleration; it may represent acceleration or a change of direction.
• Reading the vertical axis of a distance‑time graph as speed – the gradient, not the axis value, gives speed.
• Neglecting sign on a velocity‑time graph; negative area represents motion opposite to the chosen positive direction.
• Thinking that density is the same as mass; density also depends on volume.
• Believing that pressure only acts on solids; it is a fundamental concept for fluids and gases as well.

17 . Practice Questions

1. Sketch a distance‑time graph for a car that:

   • starts from rest,
   • accelerates uniformly for 4 s to a speed of 12 m s⁻¹,
   • then travels at that speed for a further 6 s.

2. From your graph, determine:

   1. The acceleration during the first 4 s.
   2. The total distance travelled after 10 s.

3. A speed‑time graph shows a constant speed of 5 m s⁻¹ for 8 s, then a uniform deceleration to rest in 2 s. Calculate the distance covered during the deceleration phase.
4. Using the velocity‑time graph below (optional), find:

   1. The acceleration between 2 s and 5 s.
   2. The displacement after 7 s.

5. A 2 kg ball is thrown vertically upward with an initial speed of 10 m s⁻¹.

   1. Calculate its kinetic energy at launch.
   2. Determine the maximum height reached (ignore air resistance).

6. Density & Pressure: A metal block (mass = 3 kg, volume = 0.0004 m³) is placed in water. Will it float? Show calculations for density and compare with water’s density (1 000 kg m⁻³).
7. Thermal physics: 0.5 kg of aluminium (c = 900 J kg⁻¹ K⁻¹) is heated from 20 °C to 80 °C. Find the heat energy supplied.
8. Wave basics: A wave has a frequency of 250 Hz and a wavelength of 0.6 m. Calculate its speed.
9. Electricity: A circuit contains a 12 V battery and a resistor of 4 Ω. Determine the current and the power dissipated in the resistor.

18 . Summary

• The gradient of a distance‑time graph = speed; the gradient of a speed‑time (or velocity‑time) graph = acceleration.
• The area under a speed‑time graph = distance travelled; under a velocity‑time graph = displacement.
• Scalar‑vector distinctions (distance vs. displacement, speed vs. velocity) are essential for correct interpretation.
• Accurate measurement (ruler, timer) and averaging give reliable data for plotting.
• Linking motion to forces (Newton’s 1st Law), momentum, energy, density, pressure, thermal physics, waves, and electricity provides a coherent framework that prepares students for the full IGCSE syllabus and later studies.