## Find the Stopping Distance of a Car

### Problem:

You are driving at 50 mph on a freeway when you wonder what your stopping
distance would be if the car in front of you jammed on its brakes. When you get home you
decide to do the calculation. You measure your reaction time to be 0.8 seconds from the time
you see the car's brake lights until you apply the brakes. Your owners' manual says that
your car slows down at a rate of 6 m/s^{2} when the brakes are applied.

Adapted from The Unversity of Minnnesota Physics and Education Research and Development Group

## Step 1) Focus on the Problem

## Stopping Distance of a Car |

## FOCUS on the Problem## Picture and Given InformationDraw a picture, identifying the useful quantities |

## Question:What distance did the car travel from when the brake light is seen to when it stopped? |

## Approach:Use the definitions of velocity and acceleration. The velocity is constant until the brakes are applied. In this time interval, the velocity is constant. When the brakes are applied the acceleration is constant, but the velocity decreases to zero. We can also note that the distance traveled by the car before the brakes were applied plus the distance traveled by the car after the brakes were applied is the solution to the problem. |

## Step 2) Describe the Physics

### Make a diagram of the situation

defining the quantities that the physics uses to describe the motion (velocity and acceleration a each interesting position and time on a coordinate system).

## Describe the Physics## Diagram(s) and define Quantities |

## Target Quantity(ies)- Stopping Distance: x
_{2}
## Possibly useful relationships |

## Step 3) Plan a Solution

### Construct the chain of equations giving a solution.

Begin with an equation containing the target quantity. Keep track of any additional unknown quantities that are introduced.

#### Quantitative Relationships

## Plan the Solution## Construct Specific Equations
Find x |

## Check for SufficiencyYes: 3 unknowns and 3 equations |

## Outline the solution steps.
Convert v |

## Step 4) Execute the Plan

### Execute the Plan

## Follow the steps Outlined in Step 3 |

## Check UnitsOur intial velocity units have been converted to m/s and all of our intermediate answers have meters as units which is correct |

## Calculate Target Quantity(s) |

## Step 5) Evalute the Solution

x_{2} is the distance traveled by the car from when the brake light is
seen to stopping. The question is answered. The answer is in meters, a correct unit of distance.
A car is about 6 meters long so 10 car lengths is not an
unreasonable distance to stop a car going that fast