A driver traveling at 25 mph in a school zone can brake to an emergency stop in 8 ft. Under similar conditions, what would be the braking distance if the car were traveling at 40 mph?
The braking distance is proportional to the kinetic energy, which means it is proportional to the square of the velocity.
So, multiply 8 ft by (40/25)^2.
You should get about 20.5 ft.
There will be an additional distance travelled while the driver responds to the emergency and applies the brake. That distance is proportional to speed, but they probably expect you to ignore it.
To determine the braking distance for a car traveling at 40 mph, we can first calculate the braking distance for the car traveling at 25 mph and then use that information to estimate the braking distance for the car traveling at 40 mph.
Given that the car traveling at 25 mph can brake to an emergency stop in 8 ft, we need to find the braking distance for the car traveling at 40 mph.
The relationship between braking distance and initial speed can be approximately described using the formula:
Braking distance ∝ (initial speed)^2
This means that the braking distance is directly proportional to the square of the initial speed. Using this relationship, we can set up a proportion to find the unknown braking distance:
(25 mph)^2 / (40 mph)^2 = (8 ft) / x
Simplifying this proportion:
625 / 1600 = 8 / x
Multiplying both sides by x:
625x = 1600 * 8
625x = 12800
Dividing both sides by 625:
x = 12800 / 625
x ≈ 20.48
Therefore, the estimated braking distance for the car traveling at 40 mph would be approximately 20.48 ft.