Enter the mass of the car, the initial velocity or current velocity, and the stopping distance to determine the braking force.

## Braking Force Formula

The following formula is used to calculate the braking force of a car given a speed, weight, and stopping distance.

F = (.5*m*v^2)/d

• Where F is the required force to stop in distnace d
• m is the mass of the car
• v is the velocity of the car before braking
• d is the stopping distance

## Braking Force Definition

Braking force is defined as the total force required to stop a car at a set stopping distance when the car is traveling at a known constant velocity.

## How to calculate braking force?

Example Problem #1

The first step to calculating braking force is to determine the mass of the car. For this example, we will say the car is an even 15,000 kg.

Next, the current velocity of the car must be measured. For this problem, the car is found to be traveling at 25m/s.

Next, determine the stopping distance. Since a different force would be required to stop the car at different distances, this is a key variable to know. In this problem we want the car to stop in 25m.

Finally, calculate the braking force using the formula above.

F = (.5*15,000*25^2) / 25

= 187,500 N = 187.5 kN

Example #2

In this next example, we will explore how the braking distance changes the force required. So, we will take the mass and the velocity of the problem above, 15,000kg and 25m/s respectively, but the braking distance is now 100m.

Using the formula, we analyze the change in force.

F = (.5*15,000*25^2)/100

= 46,875 N

This may not be immediately apparent to your eye, but the stopping force is exactly 1/4 of that from example 1 because the stopping distance is 4 times that from example 1.

In other words, the stopping distance is inversely proportional to the braking force.