# Stopping Distance Formula

## What is Stopping Distance Formula?

Imagine a car is travelling on a straight road, but suddenly there is a speed breaker which we could not notice and saw it almost near to the obstacle. Thus the stopping distance is the distance that the car.

travels from the moment that the brakes are applied to the moment that the car stops suddenly before it strikes the speed breaker. The formula used to calculate this distance is known as the stopping distance formula and it is also known as the braking distance and the braking distance equation.

Therefore, the stopping distance can be defined as when the object or any vehicle is moving with a uniform velocity and suddenly brakes are applied. In such cases, we have noticed that the body stops completely after covering a certain distance, such distance is known as the stopping distance and the corresponding formula is the stopping distance formula or braking distance formula.

### Braking Distance Formula

We have noticed many times while travelling in a car or bus when a driver uses the brakes of a car (or bus), the car will not get deaccelerated immediately or in other words, the car will not come to rest immediately. The stopping distance is the total distance the car or any moving object covers before it comes to the rest. It is based on the velocity of the car and the coefficient of friction between the tyres and the road. This stopping distance formula does not incorporate the effect of anti-lock brakes or brake pumping.

So, stopping distance definition suggests that, when the body or in particular a vehicle is moving with a certain velocity and suddenly the driver applies brakes. We will observe that the body stops or arrives at rest entirely after covering a certain distance and this is known as the stopping distance.

In other words, we can say the stopping distance is the total distance covered within the time when the body decides to stop a moving object or a moving vehicle and the time when the vehicle stops or comes to rest entirely. The stopping distance is related to factors which are containing road surface, and reflexes of the car’s driver and it is denoted by d. Since the stopping distance is basically the distance covered, hence the SI unit for stopping distance meters (m).

### Stopping Distance Equation:

We know that according to the definition of the stopping distance, it is the total distance travelled between the time when the body decides to stop a moving vehicle and the time when the vehicle stops completely. The stopping distance is denoted by the letter d.

Now, the stopping distance equation is given by the following formula:

$\Rightarrow d=\frac{v^{2}}{2\mu g}$

Where,

v -The velocity of the vehicle

μ -The coefficient of friction

g -The acceleration due to gravity

The stopping distance formula or the braking distance formula is also given by the following equation:

d= k v2

Where,

k- The constant of proportionality

v- The velocity of the vehicle

So, we can determine the stopping distance of any vehicle if we know the velocity of the moving vehicle. We can use either of the formulae in order to calculate the stopping distance.

## Factors Affecting the Stopping Distance:

After discussing the stopping distance formula or stopping distance equation, we notice that there are certain parameters that affect the stopping distance. Let us have a look at the factors affecting the stopping distance.

### 1. Weather:

In poor weather conditions such as during the rainy season or snowfall, a car or any other vehicle will be having trouble with brakes and the total stopping distance is likely to be longer for a number of reasons. According to recent research, it suggests that the braking distances may be increased in wet conditions and another fact is this may be around multiplied by 10 on snow or ice. This means, in the snow or icy roads, it could take you further than the length of seven football pitches to stop from 70mph.

Another important fact is road conditions, which might be a factor that will affect the stopping distance. We can predict the weather conditions but we can not predict the road conditions, it is not always as clear as bad weather equals long stopping distances, either. A road might be particularly greasy or slippery if it has been raining for a long time after a period of hot weather, or if the oil has been spilt on it.

### 3. Driver Condition:

The driver's condition is the most important factor because driving requires good eyesight. A driver’s age, how aware they will be while they are driving and if they have taken or consumed any drugs or alcohol can all influence how quickly it takes them to react.

### 4. Car Condition:

Even though now we have advanced technologies to build the car and at the same time many modern cars may indeed be able to stop at considerably shorter distances than the official Highway Code states, a car’s condition can also have an important impact on the stopping distance.

### Example:

1. A Driver in a Car on a Residential Street is Travelling At 45km/h per. The driver puts on the brakes when he sees a stop sign. If the coefficient of friction between the tyres and the road is μ =0.5, then, what is the stopping distance of the car?

Sol:

Given,

The velocity of the car = 45 km/h

The coefficient of friction = μ = 0.5

The acceleration due to gravity =g = 9.8 m/s2

Now, we are asked to determine the total stopping distance of the car. We know that the stopping distance of a car is given by the total stopping distance formula:

$\Rightarrow d=\frac{v^{2}}{2\mu g}$……(1)

Where,

v -The velocity of the vehicle

μ -The coefficient of friction

g -The acceleration due to gravity

Substituting all the required values in the above equation, we get:

$\Rightarrow d=\frac{v^{2}}{2\mu g}=\frac{(45)^{2}}{2\times0.5\times9.8}$

d=206.6 m ≃207 m

Therefore, the stopping distance of the car is 207 m.