A vehicle traveling at 40 km/h requires how much more stopping power than one traveling at 20 km/h?

The relationship between a vehicle's speed and the distance required to stop is non-linear and follows the principle that stopping distance increases with the square of the speed. This means that if the speed of a vehicle doubles, the stopping distance does not simply double; it actually increases by a factor of four.

When comparing a vehicle traveling at 40 km/h to one traveling at 20 km/h, the vehicle at 40 km/h is moving at double the speed. Since stopping distance is proportional to the square of the speed, we can analyze the stopping power required:

1. At 20 km/h, the stopping distance is proportional to (20)^2, which equals 400.

2. At 40 km/h, the stopping distance is proportional to (40)^2, which equals 1600.

Therefore, the stopping distance at 40 km/h is four times that at 20 km/h. Consequently, the stopping power required for a vehicle traveling at 40 km/h is also four times greater than that of a vehicle traveling at 20 km/h. This illustrates why the correct answer is that a vehicle traveling at 40 km/h requires four times more stopping power compared to one traveling at 20 km/h.