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Physics Quiz:
Annoying Anne is driving through a residential area at exactly the limit of 20 mph.
A child jumps into the street.
Anne reacts as fast as humanly possible and manages to stop the car right before she'd hit the child.
Normal Norman is driving through the same residential area at 25 mph, just 5mph over the limit.
A child jumps into the street at the exact same distance as before.
Norman reacts exactly as fast as Anne, and has the same car, tires and brakes.
How fast will Norman's car be when he hits the child?
Answer
25mphExplanation
Total stopping distance consists of reaction distance (how far your car travels while you react) and braking distance (how far your car travels while you're standing on the brakes until it's stopped).The total stopping distance at 20 mph is shorter than the reaction distance at 25 mph.
Human reaction time is ~0.25 seconds.
At 20 mph, you're going ~29 ft per second, so you go ~7.3 ft before you can react.
At 25 mph, that's ~37 ft per second, so ~9.2 ft before you can react.
The internet says a good car can break at about 15 f/s^2.
At 29 f/s, that comes out to a stopping distance of ~28 ft.
At 37 f/s, that's ~46 ft.
So Anne, who's annoying for some reason, needs a total of ~35 ft to stop just before hitting the child.
Norman needs ~9 ft to start decelerating, so by the time he reaches the 35 ft mark (after ~26 ft of hitting the brakes,) it's been a total of ~0.98 seconds, and he is going ~26 f/s, which is ~18 miles per hour.