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How fast is Usain Bolt?

Let's start with a definition: How to define who is the fastest man in the world? We know it's Usain Bolt but why? How fast is Usain Bolt?
The fastest man in the world is defined as the person who holds the world record in the 100 meters, because it is the official sprint event where the speed will be the highest. The fastest man in the world is therefore Usain Bolt, since he holds the speed record for this 100-meter sprint. This world record was set in 9 seconds 58 hundredths.
We can then calculate several speed indicators for this race: average speed, maximum speed and also acceleration.

Calculation of Usain Bolt's average speed

Let's start with a rather simple calculation. We use the formula that says average speed is distance divided by time. This then allows us to write this formula in the form v=d/t. So we have a distance of 100 meters divided by 9,58 seconds which gives us 10,43 meters per second.

This result is not very telling. It must therefore be converted into kilometers per hour (km/h). If we travel 10,43 meters in one second (this is what 10,43 meters per second means), it means that in one minute we travel 60 times more and in one hour we travel 60 x 60 = 3600 times more. We therefore obtain 10,43 x 3600 = 37 meters in one hour. We divide by 548 to obtain kilometers, which gives a average sprint speed at 37,548 km/h.

Let's go back to this calculation. So we first multiplied by 3600 to go from seconds to hours and then divided by 1000 to go from meters to kilometers. All you have to do is multiply meters per second by 3600/1000 = 3,6 to get kilometers per hour. 10,43 x 3,6 = 37,548 km/h.

Some comparisons

  • For 3 weeks, the Tour de France goes at an average speed of 40,22 km/h (source Team)
  • The length of a marathon is 42,195 kilometers. The world record is 2 hours 1 minute and 39 seconds = 2,0275 h. We obtain an average speed of 20,811 km/h
  • The average speed of a car in Paris is 14 km/h. That of the metro fluctuates between 20 and 40 km/h. When you're Usain Bolt and you're in Paris, it's better to run!
  • Finally, Usain Bolt has the speed of a cat. The average speed of a cat is 38 km/h when running a long enough distance

Calculation of Usain Bolt's maximum speed

The maximum speed in practice is not calculated. In any case, not for this example there. From a mathematical point of view, when the maximum speed is reached, the derivative cancels out (however, it is not because the derivative cancels out that the speed is maximum, it can also be zero or just reach a plateau ).

So here we are going to cheat a little. Le Monde tells us that Usain Bolt's top speed is 44,72 km/h. It is therefore between the wolf (50 km/h) and the alligator (32 km/h) and would therefore not be ridiculous running alongside a car in built-up areas. This time, he is beaten to the hilt by the subway and the car at top speed.

Acceleration approximation

Researchers have shown (here is the article for the more seasoned) that the maximum speed could be reached in about 5 seconds of running. As we saw above, the maximum speed of Usain Bolt is 44,72 km/h or dividing this time by 3,6, we can say that it is 12,4 m/s. If we assume that its acceleration is constant, then it will be 12,4 / 5 = 2,48 m / s2 = 8,9 km/h/s. If we translate this into French, it means that every second Usain Bolt increases his speed by 8,9 km/h.
However, to make this calculation it was assumed that the acceleration is constant. But this is not the case, so at the height of its acceleration, it must have exceeded 10 km/h per second.

To complete these figures a little, we learn about this paper, that Usain Bolt is not very aerodynamic, that he develops to his maximum a power of 2619,5 W and that he could have improved his time because he has a headwind of 0,9 m/s, which slows him down.

Do you want to go further on the notion of speed? Here is our article on thequadratic equation

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