When you double your speed from 20 to 40 mph, your vehicle’s braking distance will become __ times longer.
Answers
Two
Three
Four
10
The Correct Answer and Explanation is :
The correct answer is Four.
When you double your speed from 20 mph to 40 mph, your vehicle’s braking distance will become four times longer. This is because the braking distance increases with the square of the speed. This relationship is described by the equation:
[
\text{Braking distance} \propto v^2
]
where ( v ) is the velocity (speed) of the vehicle.
To break this down:
- At 20 mph, the braking distance is based on a certain factor. For example, if it takes 20 feet to stop from 20 mph, we can assume that the braking distance at this speed is ( D_{20} ).
- When the speed is doubled to 40 mph, the braking distance becomes proportional to the square of the speed. So, we calculate the braking distance at 40 mph as:
[
\text{Braking distance at 40 mph} \propto (40)^2 = 1600
]
[
\text{Braking distance at 20 mph} \propto (20)^2 = 400
]
Therefore, the braking distance at 40 mph is:
[
\frac{1600}{400} = 4
]
Thus, the braking distance at 40 mph is four times longer than at 20 mph.
This happens because at higher speeds, the vehicle needs more time to decelerate, and since the kinetic energy of a vehicle is proportional to the square of its speed, it takes exponentially more distance to stop as speed increases. Essentially, the faster you are going, the greater the force needed to stop, and the more distance it takes to overcome that momentum.
This principle underscores the importance of adjusting driving habits as speed increases, particularly in terms of leaving sufficient distance from other vehicles for safe stopping.