Stopping Distance Formula

Imagine that a car is traveling on a straight road, but there is a speed breaker on the road which the driver failed to see and noticed when the car got too close to the obstacle. So, the driver hastily applies the brake of the car and brings the car to a sudden stop. This situation where the car is brought to a stop under constant application of a braking force is known as deceleration and the distance the car travels to come to a stop is known as stopping distance.

So, the stopping distance is the distance that the car travels from the moment that the driver applies the brakes to the moment that the car comes to a stop. The formula which is used to calculate this distance is known as the stopping distance formula and it is termed as the braking distance that is widely used in automobile industries.

Stopping Distance formula

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:

⇒ d = v²/2μg

⇒ d=v²2μg

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.

2. Road Condition 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 spilled 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 \[\frac{m}{s^{2}}\]

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:

d = v²/2μg. ……(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:

d = v²/2μg

(45*45)/ 2×0.5×9.8

⇒ d = 206.6 m ≃ 207 m

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

The following factors affect the stopping distance and are very important with regard to the safety of the people that are inside the car. These factors are:

1. Weather – The Weather plays a crucial role while determining the stopping distance as the friction coefficient of the road changes along with the changing weather condition.

2. Road Condition – If the condition of the road is not in a good condition, it is far more probable that the car is at risk of an accident.

3. Condition of the Driver – The Driver of the Car has a very important role and his personal reflex actions must be considered while determining the stopping distance.

4. Condition of the Car – The stopping distance of every car differs as no two cars are in the same condition and hence their stopping distance will differ from each other. Proper servicing of the car is very important.

This is how stopping distance is calculated by deriving the formula considering all the physical conditions. Focus on the meaning of each physical term used to calculate the formula to understand how to use it.