You don’t have to be a mathematician to figure out your braking distance. But you do need to know some simple equations.
Why Does Braking Distance Quadruple When Speed Doubles? Your braking distance will quadruple when your speed doubles because the work that it takes to stop your car means removing all of the kinetic energy. That means that for a fixed maximum braking force, your braking distance will be proportional to the square root of the velocity.
We’ll go into more detail about this in a moment. But first, let’s go over some important equations.
Forces and Braking
Let’s begin by discussing stopping distances.
If you find yourself in an emergency situation in your vehicle, it’s obviously important that you can bring your car to a stop in the shortest possible distance. If you need to stop, you hit the brake and hope the car stops in time.
Researchers have an equation for this, and it looks like this: stopping distance = thinking distance + braking distance
So what is the thinking distance? Well, in our equation, your thinking distance is the distance your car travels in the time it takes you to apply the brakes after realizing that you need to stop.
Your braking distance is something different. In our equation, your braking distance is defined as the distance your car travels in the time after you have applied the brakes.
Reaction times
Reaction times are going to vary from driver to driver, but generally speaking, reaction times are typically between 0.2s and 0.9s.
There are many factors that can affect your reaction time. Some of those factors include:
- How tired you are
- Distractions
- Alcohol
- Drug use
The longer your reaction time, the higher your thinking distance is what the researchers would say.
You can measure reaction time in several different ways. One thing you can do to measure your reaction time involves dropping a ruler between your open thumb and forefinger. The more time that you need to react to the falling ruler, the further the ruler will fall before being stopped.
Your braking distance
There are a few different factors that can affect your car’s braking distance. Some of those factors might include:
- Wet or icy roads
- Weather conditions, such as rain
- Worn tires or brakes
When you apply force to the brakes of your car, work is created by the friction between the wheel and brakes. This motion will reduce the kinetic energy of your car. That means that your vehicle will slow down. It also means that the temperature of your brakes will increase.
The faster you are traveling, the more braking force you will need to stop your car at a certain distance. The greater your braking force is, the greater your deceleration will be.
It’s worth noting that large decelerations can cause your brakes to overheat. Applying a greater brake force could also cause you to lose control of the vehicle.
General stopping distances
While we’re discussing typical stopping distances, it’s important that you know how to estimate the stopping distance for your car that will vary with different speeds.
Here are some typical stopping distances.
If you are traveling at 20 miles per hour:
- Your thinking distance will be 6m
- Your braking distance will be 6m
- Your total stopping distance will be 12m
If your car is traveling at 40 mph:
- Your thinking distance will be 12m
- Your braking distance will be 24m
- Your total stopping distance will be 36m
And if your vehicle is traveling at 70 mph:
- Your thinking distance will be 21m
- Your braking distance will be 75m
- Your total stopping distance will be 96m
It’s worth mentioning again that the thinking distance will always be proportional to the starting speed. The reason for this is that reaction time is considered a constant. And speed = distance x time.
Remember that the braking distance will increase four times every time that the starting speed doubles.
Here’s an example of that: If you double your car’s speed from 30 mph up to 60 mph, your thinking distance will double from 9m to 18m. And your braking distance will then increase by a factor of four. So it will go from 14m to 56m.
If you want another explanation, check out this video.
How to Calculate Stopping Distances
There are some simple equations that you should know when you’re trying to calculate stopping distance. You should be able to estimate how the stopping distance for your car will vary at different speeds. You will also learn how to calculate the work done in bringing your moving vehicle to a stop.
Your braking force
Don’t forget that your braking distance will increase four times every time that your starting speed doubles. The reason for this is that the work done in bringing your vehicle to a stop means that it is removing all of its kinetic energy.
The equations look like this:
Work done = kinetic energy
Work done = braking force x distance
W = F x d
Kinetic energy = 1/2 x mass x (velocity)2
KE = 1/2 x m x v2
That also means that:
F x d = 1/2 x m x v2
All of that comes down to the fact that the braking distance is proportional to the square root of the velocity for a fixed max braking force.
Thinking distance calculation example
Let’s say that your car is traveling at 12 m/s. Your reaction time is 0.5s. Suddenly, a dog or a child runs out in front of your car. What would the thinking distance be as you react?
Well, we start with the equation distance = speed x time.
d = v x t
d = 12 m/s x 0.5s
In this example, your thinking distance will be 6m.
Braking distance calculation example
In the previous example, your car has a total mass of 900 kg. If your braking force is 2,000 N, what would your braking distance be?
F x d = 1/2 x m x v2
d = 1/2 x (m x v2)/F
d = 1/2 x 900 x (12)2/2,000
That means that your braking distance will be 32m.
Stopping distance calculation example
Now that you know the braking distance and the thinking distance, what about the stopping distance?
Well, the stopping distance is going to be the thinking distance plus the braking distance.
Stopping distance = thinking distance + braking distance
Stopping distance = 6 + 32
Stopping distance = 38m
So Then How Does Speed Affect Stopping Distance?
It’s important to note that as your speed increases, you will also increase the force of impact. When the speed of an object remains constant, and the weight of the object increases, it will increase the force of impact.
In other words, the faster you are moving, the longer distance you will need to stop. As we’ve been discussing today, when your car’s speed doubles, you will need four times the distance to stop. By that same measure, if your car’s speed triples, you will need nine times the distance to stop.
Weight works very similarly to speed when it comes to stopping distances. That means that when you increase the weight of an object, the distance needed to stop your vehicle will also increase.
Here are a few things to keep in mind:
- Both higher speeds and higher weights will increase your stopping distance
- Higher speeds and higher weight reduce the control you have in driving accidents
- Higher speeds and higher weight will also increase the force of impact if you have a collision
It All Comes Down to This
The speed that you are driving is directly proportional to thinking distance and braking distance. When you are driving faster you will have to cover more ground before you can react to an emergency. You will also need more distance to come to a full stop. Hopefully, now you better understand why your braking distance will quadruple when your speed doubles. Be safe out there!