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How fast?

Forces and motion · level 4, lesson 1 of 6

A question to start

Standing still on the equator, you are moving. The Earth spins once a day, and carries you round with it. How fast are you going? Would you go faster or slower standing on the equator of Mars?

The idea

Speed is how far something goes in a certain time:

\[\text{speed} = \frac{\text{distance}}{\text{time}}.\]

If distance is in metres and time in seconds, speed is in metres per second, m/s. In kilometres and hours, it is in km/h. To change between them:

  • m/s to km/h: multiply by 3.6 (there are 3,600 s in an hour and 1,000 m in a km).
  • km/h to m/s: divide by 3.6.
distancespeedtime

The triangle helps you remember: cover the one you want. Distance = speed × time; time = distance ÷ speed.

Back to the spinning planets. A point on the equator goes once round the planet in one day:

A point on the equator Mars Earth
Distance round the equator 21,340 km 40,075 km
Time for one turn 24.6 h 23.9 h
Speed 867 km/h, 241 m/s 1,674 km/h, 465 m/s

Mars is about half Earth's width and turns in about the same time, so its equator moves about half as fast. You don't feel it, because everything around you moves with you.

Worked examples

1. Perseverance. At top speed it covers 152 m in an hour. In m/s: \(152 \div 3600 = 0.042\) m/s, about 4 cm a second.

2. A runner. 100 m in 12.5 s: \(100 \div 12.5 = 8\) m/s. In km/h: \(8 \times 3.6 = 28.8\) km/h.

3. Light from the Sun to Mars. Light moves at 300,000 km/s. Mars is on average 228 million km from the Sun. Time \(= 228{,}000{,}000 \div 300{,}000 = 760\) s, about 12.7 minutes.

Try it

  1. A cyclist goes 6 km in 20 minutes. What is the speed in km/h?
  2. Change 20 m/s to km/h.
  3. Change 90 km/h to m/s.
  4. How long does Perseverance take to drive 500 m at top speed?
  5. A dust storm front on Mars moves at 20 m/s. How far does it go in an hour?
Answers
  1. 20 minutes is a third of an hour: \(6 \times 3 = 18\) km/h.
  2. \(20 \times 3.6 = 72\) km/h.
  3. \(90 \div 3.6 = 25\) m/s.
  4. \(500 \div 152 = 3.3\) hours, about 3 h 17 min.
  5. \(20 \times 3600 = 72{,}000\) m, which is 72 km.

Common mistake

Mixing units. A speed in km/h times a time in seconds gives nonsense. Change everything into matching units first: metres with seconds, or kilometres with hours.

Where it leads