By how much does the braking distance increase when you triple your speed from 20 to 60 mph?

When considering how braking distance increases with speed, it's important to understand the physics involved. The braking distance is not a linear function of speed; instead, it is proportional to the square of the speed. This means that if you increase your speed, the distance required to stop increases significantly.

In this case, when you triple your speed from 20 mph to 60 mph, you can calculate the braking distance increase by using the formula for braking distance, which is roughly proportional to the square of the speed.

Starting at 20 mph:

• The braking distance at 20 mph can be represented as ( d_1 \propto (20)^2 = 400 ).

When you triple that speed to 60 mph:

• The braking distance at 60 mph becomes ( d_2 \propto (60)^2 = 3600 ).

Now, by comparing the two distances:

• The ratio of braking distances is ( \frac{d_2}{d_1} = \frac{3600}{400} = 9 ).

This shows that when you triple your speed from 20 mph to 60 mph, the braking distance increases by a factor of 9. Therefore, the correct choice highlights the relationship between