Speed: v = s/t

Beta · Lesson 11/09 · IGCSE 0653

Physics · IGCSE Combined Science 0653

Warm-up

5 minutes

  • You and a friend leave Piazza Maggiore together.
  • One walks, one cycles, one drives.
  • Who arrives first — and how do we know, without a stopwatch?
DEFINITION
v=\dfrac{s}{t}

s = distance (m)    t = time (s)    v = speed (m/s)

Common unit: km/h
km/h → m/s: ÷3.6    m/s → km/h: ×3.6

Worked example — direct

Bologna → Firenze ≈ 100 km, in 1 hour

1
v=s/t
2
v=100\ \mathrm{km}/1\ \mathrm{h}=100\ \mathrm{km/h}
average speed
3
100\div 3.6\approx 27.8\ \mathrm{m/s}
convert to SI units

Worked example — inverse

Cyclist at 20 km/h, distance 5 km

1
t=s/v
2
t=5/20=0.25\ \mathrm{h}
not minutes yet!

0.25 h ≠ 25 minutes → it's 15 minutes.

Try it yourself (1/2)

  • 1. A car travels 180 km in 2 h — find v in km/h and in m/s.
  • 2. A runner moves at 4 m/s for 10 minutes — how many metres does she cover?

Try it yourself (2/2)

  • 3. A train travels at 120 km/h — how long to cover 300 km? Give hours and minutes.
  • 4. Convert 15 m/s into km/h.
02

Distance–time graphs

Reading a distance–time graph

  • Slope of the line = speed
  • Steeper line → faster motion
  • Flat line → object is stationary
  • Downward slope → moving back the other way

Read the graph — Cambridge IGCSE style

Distance-time graph: car and bicycle
  • (i) Use Fig. 9.1 to describe the car journey.
  • (ii) State the time at which the bicycle passes the car.
Source: Cambridge IGCSE Combined Science 0653, past paper (Fig. 9.1). The car and bicycle start from the same point, same direction, same road.
03

Quick check

Quick check — multiple choice

A man climbs up a vertical cliff that is 60 m high. He takes two hours to reach the top. What is the average vertical speed of the man?

  1. 0.0083\ \mathrm{m/s}
  2. 0.50\ \mathrm{m/s}
  3. 30\ \mathrm{m/s}
  4. 120\ \mathrm{m/s}
v = 60 m ÷ (2×3600 s) = 60/7200 ≈ 0.0083 m/s. Il trabocchetto è dimenticare di convertire le ore in secondi.
Source: Cambridge IGCSE Combined Science 0653, past paper.

Quick check — calculation

Answer in m/s

  • A cyclist travels 30 km in 2 hours.
  • What is her average speed?

Summary

  • Average speed: v = s/t
  • SI unit m/s · common unit km/h · convert ÷ or × 3.6
  • On a distance–time graph, slope = speed