Seventy Versus One Hundred

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Additionally, some earlier writings:

Supposed two identical cars are traveling along the same straight road, with one traveling at 70 kilometres an hour, the other at 100 kilometres an hour. Just as the faster car draws roughly level with the slower, they both see an obstruction in the road ahead, and (as luck would have it) at the exact same moment, exactly when they are level with each other, they both slam on the brakes.

The slower car manages to stop in time, just at the obstacle. The faster car of course does not stop in time, and the question is:

At what speed does the faster car
hit the obstruction?

You might choose at this point to go away and think about it for a bit, but for those who simply want the answer, scroll down ...

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(keep scrolling ...)

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(was that far enough?)

Clearly there are lots of confounding factors here, and it's impossible to give an exact, precise, and accurate answer. However, we can make some reasonable assumptions and see what we get.

So what are some reasonable assumptions? Here are the assumptions I used.

In truth, this is not a good assumption. They are more likely to shed energy at a constant rate with time, not with distance, but we'll get to that.
Let's assume that the brakes are working at their limit, and as they do so, they are shedding energy at a maximum rate that doesn't change. The cars are identical, so they are both shedding energy at the same rate per unit distance.

We don't know how much energy they have, but with one doing 70 and the other doing 100, we know that the faster one has roughly twice the (kinetic) energy of the slower. Roughly.

The slower car sheds its energy in time. In that same distance, the faster car will shed the same amount of energy (by our assumption) so:

It still has half its energy left
when it reaches the obstacle.

So it's still doing about 70 when it crashes.

Ouch.

So what if the rate of shedding energy is not per unit distance, but per unit time? That's significantly worse. The faster car reaches the obstacle in less time (because that's what "faster" means) so it has less time to shed energy, so it has even more left.

How much? Good question. Let me know your answer ...

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