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 carâ€™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 weâ€™ve already mentioned, stopping distances can be influenced by a number of factors.

- Weather: In poor weather conditions, a carâ€™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 â€“ 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.
- Road condition: Itâ€™s not always as clear as â€˜bad weather equals long stopping distancesâ€™, 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.
- Driver condition: A driverâ€™s age, how awake they are and if theyâ€™ve consumed any drugs or alcohol can all influence how quickly it takes them to react.
- Car condition: While many modern cars may indeed be able to stop in shorter distances than the official Highway Code states, a carâ€™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

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