Honors Physics

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/s2 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 Information

Braw a picture, identifying the useful quantities

Sketch 1
First Diagram of the Problem

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

Sketch 2
Diagram of the Physics

Target Quantity(ies)

  • Stopping Distance: x2

Possibly useful relationships

equations
Useful Equations
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 x2:
The stopping distance x2 is given by:
Equation 1

Find x1:
Equation 2

Find D:


Unknowns:
x1, D, x2

Check for Sufficiency

Yes: 3 unknowns and 3 equations

Outline the solution steps.

Convert v1 to m/s
Using equation (3) Solve for D and put into equation (1)
Using equation (2) Solve for x1 and put into equation (1)
Using equation (1) solve for x2

Step 4) Execute the Plan

Execute the Plan

Follow the steps Outlined in Step 3

Conversion
Given Information
Step 1
Step 2

Check Units

Our 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)

Result
Step 5) Evalute the Solution

x2 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