Determine, qualitatively, from given data or the shape of a distance-time graph or speed-time graph when an object is: (a) at rest (b) moving with constant speed (c) accelerating (d) decelerating

Cambridge IGCSE Physics 0625 – Motion, Forces & Energy (Core)

1. Physical Quantities, Units & Measurement

• Length / distance (s) – metre (m)
• Time (t) – second (s)
• Mass (m) – kilogram (kg)
• Speed / velocity (v) – metre per second (m s⁻¹)
• Acceleration (a) – metre per second squared (m s⁻²)
• Force (F) – newton (N)
• Energy / work (E, W) – joule (J)
• Power (P) – watt (W)
• Density (ρ) – kilogram per cubic metre (kg m⁻³)

SI prefixes (useful for AO2 calculations): k (10³), h (10²), da (10¹), d (10⁻¹), c (10⁻²), m (10⁻³), µ (10⁻⁶), n (10⁻⁹).

Record every measurement with the correct unit and an appropriate number of significant figures (AO1).

2. Scalars vs. Vectors

• Scalar: magnitude only (e.g. speed, distance, mass, energy).
• Vector: magnitude + direction (e.g. velocity, displacement, force, momentum).

3. Motion – Key Definitions & Equations

4. Mass, Weight & Density

• Mass (m) – amount of matter; invariant, measured in kg.
• Weight (W) – force of gravity on a mass; \(W = mg\) (N).
• Gravitational field strength (g) – weight per unit mass; \(g = \dfrac{W}{m}\) (N kg⁻¹), numerically ≈ 9.8 N kg⁻¹ near Earth’s surface.
• Density (ρ) – mass per unit volume; \(\rho = \dfrac{m}{V}\) (kg m⁻³).

Example: A wooden block has \(m = 0.45\ \text{kg}\) and \(V = 2.0\times10^{-4}\ \text{m}^3\).

\(\rho = 0.45 / 2.0\times10^{-4} = 2250\ \text{kg m}^{-3}\). Since \(\rho{\text{wood}} > \rho{\text{water}} (1000\ \text{kg m}^{-3})\), the block will sink.

5. Forces

• Resultant (net) force – vector sum of all forces acting on an object: \(\displaystyle \sum\vec F\).
• Weight – acts vertically downwards; magnitude \(mg\).
• Normal reaction (R) – contact force perpendicular to a surface.
• Friction

  • Static friction – prevents motion up to a maximum value \(fs^{\max}= \mus R\).
  • Kinetic friction – acts when sliding; magnitude \(fk = \muk R\).

• Tension – pulling force transmitted through a string, rope or cable.
• Moment (torque) M – turning effect of a force: \(M = F \times d\) (where \(d\) is the perpendicular distance from the pivot).
• Centre of gravity – point at which the weight of an object can be considered to act; for uniform objects it coincides with the centre of mass.
• Equilibrium – when \(\sum\vec F = 0\) and \(\sum M = 0\); the object either remains at rest or moves with constant velocity.

Practical tip: Opening a door is easier when the force is applied far from the hinges because the moment \(M = Fd\) is larger.

6. Energy, Work & Power

7. Practical / Experimental Skills (AO3)

1. Suggested practical – ticker‑timer or video analysis

   • Set up a straight track and attach a ticker tape (or record a video).
   • Release the object (e.g., a toy car) from rest.
   • Count the dots (each dot = 0.02 s) or use video‑analysis software to obtain position at equal time intervals.
   • Plot distance vs time and/or speed vs time.
   • Determine gradients to find speed(s) and acceleration(s).

2. Data‑handling checklist

   • Use consistent units throughout.
   • Label axes clearly (including units).
   • Draw best‑fit straight lines where appropriate; state the equation of the line.
   • Estimate uncertainties and discuss likely sources of error (e.g., reaction time, friction, air resistance).

8. Qualitative Interpretation of Graphs (AO2)

8.1 Distance‑time graphs

8.2 Speed‑time graphs

8.3 Quick Checklist for Students

1. Identify the axes – distance vs time or speed vs time.
2. Vertical position:

   • Zero speed → at rest.
   • Non‑zero constant → constant speed.

3. Gradient (slope):

   • Zero gradient on a distance‑time graph → at rest.
   • Constant non‑zero gradient → constant speed.
   • Increasing gradient → accelerating.
   • Decreasing positive gradient → decelerating.

4. On a speed‑time graph the gradient is the acceleration:

   • Positive → accelerating.
   • Negative → decelerating.
   • Zero → constant speed (or rest if the speed value itself is zero).

8.4 Worked Example – Distance‑time graph

Problem: A cyclist’s distance‑time graph shows:

– 0 s → 2 s: horizontal line

– 2 s → 6 s: straight line with slope = 4 m s⁻¹

– 6 s → 10 s: curve that flattens.

Answer:

• 0 s – 2 s: horizontal → at rest.
• 2 s – 6 s: straight line, constant slope → constant speed of 4 m s⁻¹.
• 6 s – 10 s: curve becoming less steep → decelerating (still moving forward).

8.5 Worked Example – Speed‑time graph

Problem: A ball rolls down a slope. The speed‑time graph is a straight line from (0 s, 0 m s⁻¹) to (5 s, 10 m s⁻¹). Find the acceleration.

Solution: Acceleration = slope = \(\displaystyle \frac{\Delta v}{\Delta t} = \frac{10-0}{5-0} = 2\ \text{m s}^{-2}\).

The ball is accelerating uniformly at \(2\ \text{m s}^{-2}\).

9. Summary Table – Graph Features vs. Motion

10. Mapping to Cambridge Assessment Objectives

11. Quick Revision Checklist

• Distinguish clearly between scalar and vector quantities.
• Memorise core equations for speed, acceleration, force, work and power.
• Be able to read and interpret distance‑time and speed‑time graphs (identify rest, constant speed, acceleration, deceleration).
• Remember that the gradient of a distance‑time graph gives speed; the gradient of a speed‑time graph gives acceleration.
• Recall the definitions of weight, mass, density, and gravitational field strength.
• Know the two types of friction and the formulae for their maximum values.
• Understand the concept of terminal velocity for falling objects with air resistance.
• Practice a simple practical (ticker timer or video analysis) and be ready to discuss sources of error and uncertainties.

These notes provide a concise, syllabus‑aligned overview of the core content for “Motion, Forces & Energy” and the essential skills required for the Cambridge IGCSE Physics examination.