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I'm not a mathematician and this is something that I've pondered for years...

If I'm travelling at 1 mile per hour, and a car beside me is travelling 2 miles per hour it will (obviously) overtake me. (I don't know how long that will actually take but for my explanation let's say 10 seconds.) As I'm only going 1 mile per hour it will likely feel like the person is travelling much faster than I am.

BUT, if I'm now travelling at 60 miles per hour and the car beside me is travelling at 61:

  1. Will it still take the same time (e.g. 10 seconds) to overtake me?
  2. Will I feel as though they are only marginally faster than I am? (If before they were travelling 100% faster than me, but this time they're only travelling roughly 1.7% faster will it feel like they're overtaking me more slowly - regardless of the actual time taken in #1?)

If you can help me finally put this to bed - THANK YOU!

Ethan
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collington
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    I'm not sure if this is on topic for this site, since it's more of a physics question than a mathematics question. (On the other hand, it's probably a question more likely to be found in a mathematics textbook than a physics textbook.) It may be on topic at https://physics.stackexchange.com/. – Tanner Swett Nov 15 '19 at 20:32
  • 1 foot 5.6 inches per second, for a grand total of 14 foot 8 inches in 10 seconds. –  Nov 15 '19 at 20:37
  • "Will I feel as though they are only marginally faster than I am?" Sadly we do not have a mathematical theory of feelings. –  Nov 15 '19 at 21:44

1 Answers1

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The time that it takes for the other car to pass your car is the ratio of the difference of speeds over the length of your car. So if your speed is $1$ and the other car's speed is $2$ and the length of your car is $0.1$, then it takes $1/0.1=10$ units of time to pass your car. It takes the same amount of time in case of speeeds being $60$ and $61$

The only differece is that within the same time period in the first case you moves 10 units of distance where in the second case you moved 600 units of distnce.

Mohammad Riazi-Kermani
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