What is Speed, by formula? — Physics

Definition 52.1 Primary & Middle School Physics · Chapter 52 — Motion Graphs and Average Speed

For a journey (or stretch of one) covered at a steady pace, the speed $v$ is the distance $d$ divided by the travel time $t$ :

v = \frac{d}{t}.

With $d$ in kilometres and $t$ in hours, $v$ speaks kilometres per hour ( $\mathrm{km}/\mathrm{h}$ ); with metres and seconds, metres per second ( $\mathrm{m}/\mathrm{s}$ ) — the scientist’s favorite. Like density’s, this formula computes in all three directions: $v = d/t$ , $d = v \times t$ , $t = d/v$ .

Examples

Example 52.2 (The recipes at work)

A train covers $240\,\mathrm{km}$ in $2$ hours: $v = 240 \div 2 = 120\,\mathrm{km}/\mathrm{h}$ . How far at that pace in $5$ hours? $d = 120 \times 5 = 600\,\mathrm{km}$ . How long for $300\,\mathrm{km}$ ? $t = 300 \div 120 = 2.5$ hours — two hours and thirty minutes (mind the rebel: $0.5$ hours is $30$ minutes, never “ $50$ ”).

Example 52.3 (Two units, one speed)

A sprinter runs $100\,\mathrm{m}$ in $10\,\mathrm{s}$ : $v = 10\,\mathrm{m}/\mathrm{s}$ . How fast is that in road units? In one hour — $3600$ seconds — the sprinter would cover $10 \times 3600 = 36\,000\,\mathrm{m} = 36\,\mathrm{km}$ : so $10\,\mathrm{m}/\mathrm{s} = 36\,\mathrm{km}/\mathrm{h}$ . The general exchange rate: each $\mathrm{m}/\mathrm{s}$ is worth $3.6\,\mathrm{km}/\mathrm{h}$ — because an hour holds $3600$ seconds and a kilometre only $1000$ metres. Sound’s $340\,\mathrm{m}/\mathrm{s}$ , in road units: over $1200\,\mathrm{km}/\mathrm{h}$ .

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Examples

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