Stopping Distance Formula

If a driver uses the brakes of a car, the car will not come to a stop immediately. The stopping distance is the distance the car covers before it comes to a stop. It is based on the speed of the car and the coefficient of friction between the wheels and the road. This stopping distance formula does not comprise the effect of anti-lock brakes or brake pumping. This lesson will explore the physics behind the distance it takes to stop a moving car. You’ll learn stopping distance formula with example.

Source:en.wikipedia.org

 

Stopping Distance Formula

Concept of Stopping Distance:

When the body is moving with a certain velocity and suddenly one applies brakes. You will observe that the body stops entirely after covering a certain distance. This is stopping distance.

The stopping distance is the distance covered between the time when the body decides to stop a moving vehicle and the time when the vehicle stops entirely. The stopping distance relates to factors containing road surface, and reflexes of the car’s driver and it is denoted by d. The SI unit for stopping distance meters.

The Formula for Stopping Distance:

Stopping Distance formula is given by,

d= \( \frac{v^{2}}{2\mu g} \)

Where

v	velocity
\(\mu\)	friction coefficient
g	acceleration due to gravity
d	distance

The stopping distance formula is also given by,

d= \(kv^{2}\)

Where,

k	a constant of proportionality
v	speed
d	distance

What other factors affect stopping distances?

As we’ve already mentioned, stopping distances can be influenced by a number of factors.

1. Weather: In poor weather conditions, a car’s total stopping distance is likely to be longer for a number of reasons. Research suggests that the braking distances may be doubled in wet conditions – and multiplied by 10 on snow or ice. That means, in the snow, it could take you further than the length of seven football pitches to stop from 70mph.
2. Road condition: It’s not always as clear as ‘bad weather equals long stopping distances’, either. A road might be particularly greasy if there has been raining after a period of hot weather, or if the oil has been spilt on it.
3. Driver condition: A driver’s age, how awake they are and if they’ve consumed any drugs or alcohol can all influence how quickly it takes them to react.
4. Car condition: While many modern cars may indeed be able to stop in shorter distances than the official Highway Code states, a car’s condition can also have an impact.

Solved Examples

Q-1: Amy, a driver in a car on a residential street is travelling at 50.0 km per hr. Amy puts on the brakes when she sees a stop sign. The coefficient of friction between the tires and the road is \(\mu = 0.60.\) What is the stopping distance of the car?

Solution: The speed of the car must be converted to meters per second:

V = 50 km per hr

Converting it we get,

V = 13.89 m per sec.

The stopping distance can be found using the following formula:

d= \(\frac{v^{2}}{2\mu g} \)

Substituting the values, we get.

d= \(\frac{13.89^{2}}{2 \times 0.60 \times 9.8} \)

d = \(\frac {192.9}{11.76}\)

d = 16.40 m

The stopping distance of the car will be 16.40 m