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Speed

AshPhys · Revision cheat sheet
AS Level9702 AS Ch.1Chapter 1: KinematicsLesson 1.1Sections 1.1

Goal: Calculate average speed in m s⁻¹ and tell it apart from instantaneous speed.

01The big picture

Average speed is the total distance travelled divided by the total time taken. In SI units it is measured in m s⁻¹.

Instantaneous speed is the speed at one moment. It is found from a distance measured over a very short time, for example a card cutting through a light gate, or from the gradient of a distance–time graph. Speed is a scalar: it has size but no direction.

Average speed [paraphrase]
Total distance travelled divided by total time taken.
Instantaneous speed [paraphrase]
The speed at a particular instant: distance over a very short time interval.

02Key equations

Average speed
v=dtv = \frac{d}{t}
km h⁻¹ to m s⁻¹
1 km h−1=1000 m3600 s=13.6 m s−11\ \mathrm{km\,h^{-1}} = \frac{1000\ \mathrm{m}}{3600\ \mathrm{s}} = \frac{1}{3.6}\ \mathrm{m\,s^{-1}}
Symbols and units
  • vvspeedm s−1\mathrm{m\,s^{-1}}
  • dddistance travelledm\mathrm{m}
  • tttime takens\mathrm{s}

03Sample problems with solutions

Sample 1 · Average speed in SI units
A car travels 150 km in 2.5 hours. Calculate its average speed in m s⁻¹.

  1. Convert to metres and seconds first:

    d=150 000 m,t=2.5×3600=9000 sd = 150\,000\ \mathrm{m}, \qquad t = 2.5 \times 3600 = 9000\ \mathrm{s}

  2. Divide:

    v=150 0009000=16.7 m s−1v = \frac{150\,000}{9000} = 16.7\ \mathrm{m\,s^{-1}}
Answer: v=17 m s−1v = 17\ \mathrm{m\,s^{-1}} (2 s.f.)
Unit check: ms=m s−1 ✓\frac{\mathrm{m}}{\mathrm{s}} = \mathrm{m\,s^{-1}}\ \checkmark

04Practice problems

  1. P1
    A sprinter runs 100 m in 9.58 s. Calculate the average speed.
    Final answer10.4 m s⁻¹
    Answer: 10.4 m s⁻¹
  2. P2
    Convert 72 km h⁻¹ to m s⁻¹.
    Final answer20 m s⁻¹
    Answer: 20 m s⁻¹
  3. P3
    A card 5.0 cm long cuts through a light gate in 0.020 s. Calculate the speed of the card.
    Final answer2.5 m s⁻¹
    Answer: 2.5 m s⁻¹
  4. P4
    A runner completes a 400 m lap in 50 s. Calculate the average speed.
    Final answer8.0 m s⁻¹
    Answer: 8.0 m s⁻¹

05Other useful information

Common mistakes

  • ✗ Wrong: Divide kilometres by hours and call it m s⁻¹.

    ✓ Right: Convert to metres and seconds first (÷ 3.6 for km h⁻¹).

  • ✗ Wrong: Average speed is the average of the speeds.

    ✓ Right: It is total distance ÷ total time.

Exam tips

  • Write the unit at every step; the unit check catches most conversion slips.

What the syllabus asks

  • 9702 topic 2: define and use distance and speed. Coursebook 1.1.

Explore: Practice questions for this lesson