Tag Archives: velocity

Cars overtaking

While cycling during one of the unseasonably sunny October days, I passed lots of cars on the opposite side of the road, but none seemed to be overtaking me. I wondered: how many more I should expect on one side compared to the other?

Making some unrealistic assumptions: I ride my bicycle at a constant speed of b mph in traffic that is constant, with evenly spaced cars (a poor assumption) travelling at a constant speed c mph (not slowing when they overtake—a realistic assumption, in my experience), the answer is easily calculated.

The unslowing cars approach from behind at a merciless relative speed of c-b mph, and those safely across the central double line zoom past at c+b mph. So, for every car I pass on the opposite side of the road, I would expect to be overtaken \frac{c-b}{c+b} times.  Continue reading

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Filed under Accessible, Maths in Life