Lesson 5 — Speed as a Rate

Speed measures how fast distance changes with time. The core idea is simple:

\(\displaystyle v = \frac{d}{t}\)   (speed = distance ÷ time)

Concepts

• Units: common speeds are in \(\text{m/s}\), \(\text{km/h}\), or \(\text{mph}\). Conversion anchors: \(1~\text{m/s} = 3.6~\text{km/h} \approx 2.237~\text{mph}\).
• Average speed over an interval is \(\displaystyle \frac{\text{total distance}}{\text{total time}}\).
• Be consistent with units. Convert time to seconds for \(\text{m/s}\) or to hours for \(\text{km/h}\)/\(\text{mph}\).

Worked examples

Example 1 — Straight compute (m/s): 150 m in 12 s.

\(v = \dfrac{150~\text{m}}{12~\text{s}} = 12.5~\text{m/s}\).

Example 2 — Convert time first: 2.4 km in 8 min. What is the speed in km/h?

\(8~\text{min} = \dfrac{8}{60}~\text{h} = 0.133\overline{3}~\text{h}\), so \(v = \dfrac{2.4~\text{km}}{0.133\overline{3}~\text{h}} = 18.0~\text{km/h}\).

Example 3 — Famous sprint: 100 m in 9.58 s (Usain Bolt world record).

\(v = \dfrac{100}{9.58} = 10.44~\text{m/s}\). In mph: \(10.44~\text{m/s} \times 2.237 \approx 23.4~\text{mph}\). In km/h: \(10.44~\text{m/s} \times 3.6 \approx 37.6~\text{km/h}\).

Try it