Speed kills / physics puzzle

[Softus]

We all know that speed alone isn't enough to cause death, and that stopping very quickly can hurt a lot, but what's your intuitive answer to the following?

A child runs into the road and falls in front of a car travelling at 30mph. The driver brakes quickly enough to stop the car with its bumper about 1mm from the stationary child, and nobody is hurt.

Under identical conditions, i.e. same weather, same car, same driver, same braking, same road, and same child, a car whose initial speed was more than 30mph would hit the child instead of stopping short. What would the impact speed be in the following example of speed at the moment of starting to brake?

32mph:

35mph:

38mph:



Please note:- although reaction times are important in real life, they would make this exercise too complicated, so please take it that the driver's reaction time is precisely zero. In practise this would increase the speed at impact, so the purpose of the exercise is still valid.

PS - If you already know the answers, perhaps you could sit on your hands for a while, so that others can have a go. Thanks.
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PPS - There is no conveyor belt anywhere in this scenario.

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Edited to make reaction times irrelevant.

 

[tim west]

Im presuming that the brakes are less effective exponentially (some inverse law applies?)at higher speeds unless the driver compensates by pressing harder on the pedal?
Though i wouldnt know the formula in order to work out the answers to the above.

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Conveyors have feelings as well

 

[oompah]

If I have read correct and your last sentence is to be read as written then the impact speed is the same as the one's in your example.

 

[Softus]

Im presuming that the brakes are less effective exponentially (some inverse law applies?)at higher speeds unless the driver compensates by pressing harder on the pedal?

For this exercise, please take it that the deceleration is the same in all cases.

i wouldnt know the formula in order to work out the answers to the above.

You don't need a formula to give your intuitive answer.

 

[tim west]

It says moment of starting to brake, i read that as the brakes are applied and starting to influence the result?

 

[Softus]

If I have read correct and your last sentence is to be read as written then the impact speed is the same as the one's in your example.

I don't think you're read it correctly.

It isn't a trick question in any way. If it helps, imagine two identical cars that are neck-and-neck at the instant that they start to brake identically. At the moment of starting to brake, one car is doing 30mph and the other is going faster. The slower cars stops in the available distance, but the faster doesn't, so What speed is the faster car doing when it hits the child?

I think the factor of reactions times is irrelevant for this, so I'll edit the first post in that respect.

 

[tim west]

I'm not sure you CAN answer that question as the first time there was no impact and you need to know an impact speed from one of the results in order to extrapolate an answer for the others.

 

[Softus]

I'm not sure you CAN answer that question as the first time there was no impact and you need to know an impact speed from one of the results in order to extrapolate an answer for the others.

I suspect that you might be getting bogged down in precision.

I chose 1mm to avoid any arguments about whether or not the car could touch the child when travelling at 0mph. The answer doesn't have to be accurate - ball park would do, and it's your intuitive answer that's important.

 

[tim west]

ok i'd say there would be a 3MPH difference between each answer then taking that the child falls at exactly the same spot and not allowing for the impact to influence the speed

3 , 6 and 9 MPH? or should that be 2, 5 and 8 MPH?

 

[Softus]

It might surprise you to hear that when the initial speed is 32mph, the impact speed is 11mph.

Armed with that knowledge, do you want to estimate the impact speed(s) when the initial speed is 35mph and 38mph?

 

[oompah]

Something to do with Newtons law of physics me thinks.

 

[Softus]

Something to do with Newtons law of physics me thinks.

You don't need to have any knowledge of physics, or physicists, to give an intuitive answer.

 

[blondini]

11
18
25

 

[tim west]

If we are using the minimum braking distance rule ie the maximum amount of braking that the car can cope with is applied then i'd be surprised that the results were linear as the brakes cannot influence a faster speed equally as well as at a slower speed. Or am i missing the point?

 

[Softus]

If we are using the minimum braking distance rule ie the maximum amount of braking that the car can cope with is applied then i'd be surprised that the results were linear

The results are not linear.

...as the brakes cannot influence a faster speed equally as well as at a slower speed. Or am i missing the point?

You're not missing the point, but you've misunderstood the effect of brakes on this question.

Now that you know the results are not linear, what's your intuitive answer to the question?