Recall and use the equation average speed = total distance travelled / total time taken

Cambridge IGCSE Physics 0625 – 1.2 Motion: Speed, Velocity & Average Speed

Learning Objective

Students will be able to:

• Recall and use the equation for average speed.
• Distinguish between speed (scalar) and velocity (vector).
• Sketch, plot and interpret distance‑time and speed‑time graphs.
• Calculate speed from the gradient of a distance‑time graph and distance from the area under a speed‑time graph.
• State the value of the free‑fall acceleration g ≈ 9.8 m s⁻² (core requirement).
• (Supplementary) Define acceleration, calculate it from a speed‑time graph and describe terminal velocity.

Key Definitions

• Distance (s) – scalar, total length of the path travelled. Unit: metre (m).
• Displacement (Δ s) – vector, straight‑line change in position (magnitude + direction).
• Speed (v) – scalar, rate of covering distance.
  Formula: \(v = \dfrac{s}{t}\) Units: m s⁻¹.
• Velocity (\(\vec v\)) – vector, rate of change of displacement.
  Formula: \(\vec v = \dfrac{\Delta\vec s}{\Delta t}\) Units: m s⁻¹ (direction required, e.g. “northward”).
• Average speed – total distance travelled divided by total time taken, irrespective of any speed changes.
  Formula: \(v_{\text{avg}} = \dfrac{D}{t}\).

Measuring Distance and Time

• Distance: ruler, tape‑measure, marked track – record in metres (m).
• Time: stopwatch or digital timer – record in seconds (s).
• Record each measurement to the appropriate number of significant figures; when dividing, keep the same number of sig‑figs as the least‑precise quantity.

Core Equations

Calculating Average Speed – Step‑by‑Step

1. Measure the total distance travelled, \(D\) (in metres).
2. Measure the total time taken, \(t\) (in seconds).
3. Insert the values into \(v_{\text{avg}} = \dfrac{D}{t}\).
4. Perform the division, keeping the correct number of significant figures.
5. Check the units: metres ÷ seconds = metres per second (m s⁻¹).

Graph‑Reading Checklist

When looking at a distance‑time or speed‑time graph, always ask:

• Is the line horizontal? → object at rest.
• Is the line straight with a constant gradient? → constant speed (or constant velocity if direction is shown).
• Is the gradient increasing? → accelerating (speed increasing).
• Is the gradient decreasing? → decelerating (speed decreasing).

Sketch‑and‑Interpret Activity

For each description, sketch the required graph and label the key features (gradient, area, motion state).

1. A car travels at a constant speed of 4 m s⁻¹ for 10 s.
2. A runner starts from rest, accelerates uniformly to 6 m s⁻¹ in 3 s, then continues at that speed for a further 5 s.
3. An object falls freely for 2 s (ignore air resistance).

Core Fact – Free Fall

g ≈ 9.8 m s⁻² downwards. This value is required for all calculations involving objects in free fall.

Supplementary: Acceleration

• Definition: acceleration is the rate of change of velocity.
  Formula: \(a = \dfrac{\Delta v}{\Delta t}\) Units: m s⁻².
• From a speed‑time graph: the gradient of a straight‑line segment equals the acceleration (positive if speed increases, negative if it decreases).
• Terminal velocity: the constant speed reached when the upward force of air resistance equals the downward force of gravity. In a speed‑time graph this appears as a horizontal line after an initial acceleration phase.
• Free‑fall with air resistance: the speed‑time graph starts with a steep gradient (≈ g) and then levels off at the terminal velocity.

Practical Tip – Measuring Average Speed

Set up a straight track of known length (e.g., 2 m). Time a toy car as it travels the full length three times, record each time, and use the average of the three measurements in \(v_{\text{avg}} = D/t\). This reinforces the link between measured distance, measured time and the formula.

Worked Examples

Practice Problems

1. A runner covers 250 m in 40 s. Calculate the average speed.
2. A motorbike travels 1.2 km in 30 s. State the average speed in m s⁻¹.
3. From a speed‑time graph, a car moves at 8 m s⁻¹ for 5 s, then accelerates uniformly to 20 m s⁻¹ over the next 5 s. Find the total distance travelled.
4. Read the distance‑time graph below (gradient = 3 m s⁻¹ for the first 4 s, then = 1 m s⁻¹ for the next 6 s). Determine the average speed for the whole 10 s.
5. An object falls freely for 2.0 s. Using \(g = 9.8\; \text{m s}^{-2}\), calculate the average speed during the fall.
6. Sketch a speed‑time graph for an object that starts from rest, accelerates uniformly for 3 s to a speed of 9 m s⁻¹, then moves at constant speed for a further 4 s. State the total distance covered.

Answers (teacher use)

1. \(v_{\text{avg}} = 250/40 = 6.25\; \text{m s}^{-1}\)
2. 1.2 km = 1200 m \(v_{\text{avg}} = 1200/30 = 40\; \text{m s}^{-1}\)
3. Distance = \(8\times5 + \frac{(8+20)}{2}\times5 = 40 + 70 = 110\) m
4. Total distance = \(3\times4 + 1\times6 = 12 + 6 = 18\) m Average speed = \(18/10 = 1.8\; \text{m s}^{-1}\)
5. Final speed = \(g t = 9.8\times2 = 19.6\; \text{m s}^{-1}\) Average speed = \((0+19.6)/2 = 9.8\; \text{m s}^{-1}\)
6. Area under the graph = \(\frac{1}{2}\times3\times9 + 9\times4 = 13.5 + 36 = 49.5\) m.

Concept‑Check Questions

• Which statement is true?
  (a) Velocity is a scalar.
  (b) Speed can be negative.
  (c) The gradient of a distance‑time graph gives speed.
  (d) The area under a speed‑time graph gives acceleration.
• Identify the motion type shown by each graph:
  – Horizontal line on a speed‑time graph.
  – Straight line with positive gradient on a speed‑time graph.
  – Curved line on a distance‑time graph.

Suggested Diagram