PT - Driving Math Lesson

Driving Math

Introduction

Math is used in many driving-related scenarios such as calculating a driver’s reaction time and how long it takes for a car to come to a complete stop. This is really good to know in order to stay safe and make sure you leave enough room in front of you to be able to stop completely if you had to.

Measurement Conversions

When dealing with units of measurement, conversions may be needed. Watch the video and take notes on the measurement conversions that you may need to use in this lesson.

Measurements Practice

Connect the measurements that are equal. Click the gray arrow in the bottom right corner to check your answers.

Reaction Time and Stopping Distance

Reaction time is the amount of time between stimulus and response. In short, how quickly can you react to an event? The average reaction time is between 0.5 and 1.5 seconds.

The reaction distance is the distance traveled by a car during the driver’s reaction time. Reaction distance is approximately 1 foot for each mph of speed but varies widely depending on the driver’s reaction time.

Example 1: What is the reaction distance for a car traveling 55 miles per hour? What is the approximate range?

The answer will be somewhere around 55 feet but there is a lot of variation depending on the driver’s reaction time.

Step 1: A car traveling 55 mph travels 55 miles in one hour. Let’s convert to feet.

There are 5,280 feet in one hour. This car will travel 55 x 5,280 = 290,400 feet in an hour.

Step 2: Let’s convert to minutes.

There are 60 minutes in an hour. This car will travel 290,400/60 = 4,840 feet in a minute.

Step 3: Let’s convert to seconds.

There are 60 seconds in a minute. This car will travel 4,840/60 = 80.67 feet in one second.

Step 4: Reaction time is approximately 0.5 to 1.5 seconds.

If the reaction time is 0.5 seconds, then the reaction distance is 80.67 x 0.5 = 40.34 feet

If the reaction time is 1.5 seconds, then the reaction distance is 80.67 x 1.5 = 121 feet

The reaction distance will be between 40.34 and 121 feet.

Example 2: Try this one on your own and then check your answer below. What is the reaction distance for a car traveling 70 miles per hour? What is the approximate range?

Convert to feet: 70 x 5,280 = 369,600 feet in an hour.

Convert to minutes: 369,600/60 = 6,160 feet in a minute.

Convert to seconds: 6,160/60 = 102.67 feet in one second.

If the reaction time is 0.5 seconds, then the reaction distance is 102.67 x 0.5 = 51.34 feet

If the reaction time is 1.5 seconds, then the reaction distance is 102.67 x 1.5 = 154 feet

The reaction distance will be between 51.34 and 154 feet.

Braking Distance

After the driver reacts, they start to brake to slow down the car. This is the braking distance. The total stopping distance will be the reaction distance and the braking distance combined.

The following formula can be used to determine the braking distance:

$LaTeX: d=\frac{s^2}{20}$ $d=\frac{s^2}{20}$

d = distance in feet

s = speed in mph

Example 1: What is the approximate braking distance for a car traveling at 50 mph? What is the total stopping distance?

$LaTeX: d=\frac{s^2}{20}$ $d=\frac{s^2}{20}$

$LaTeX: d=\frac{50^2}{20}$ $d=\frac{50^2}{20}$

$LaTeX: d=\frac{2500}{20}$ $d=\frac{2500}{20}$

d = 125 feet

The reaction distance will be approximately 50 feet.

The total stopping distance will be approximately 125 + 50 = 175 feet.

Example 2: Try this one on your own and then check your answer below. Mari is driving 45 mph and sees an accident directly in front of her about 200 feet away. Will she be able to stop in time?

$LaTeX: d=\frac{s^2}{20}$ $d=\frac{s^2}{20}$

$LaTeX: d=\frac{45^2}{20}$ $d=\frac{45^2}{20}$

$LaTeX: d=\frac{2025}{20}$ $d=\frac{2025}{20}$

d = 101.25 feet

The reaction distance will be approximately 45 feet.

The total stopping distance will be approximately 101.25 + 45 = 146.25 feet.

Yes, she will most likely be able to stop in time.

Example 3: Now, let's put it all together! What is the approximate stopping distance range for a driver traveling at 75 mph?

Step 1: Find the braking distance

$LaTeX: d=\frac{s^2}{20}$ $d=\frac{s^2}{20}$

$LaTeX: d=\frac{75^2}{20}$ $d=\frac{75^2}{20}$

$LaTeX: d=\frac{5625}{20}$ $d=\frac{5625}{20}$

d = 281.25 feet

Step 2: Find the reaction distance range

Convert to feet: 75 x 5,280 = 396,000 feet in an hour

Convert to seconds: 396,000/3600 = 110 feet in a second

If the reaction time is 0.5 seconds, then the reaction distance is 110 x 0.5 = 55 feet

If the reaction time is 1.5 seconds, then the reaction distance is 110 x 1.5 = 165 feet

Step 3: Find the stopping distance using the reaction distance range

281.25 + 55 = 336.25

281.25 + 165 = 446.25

The approximate stopping distance range will be between 336.25 and 446.25 feet.

Test YOUR Reaction Time!

Try this experiment to test your reaction time! You will need a ruler and a friend.

Have your friend hold the ruler in the air and put your fingers at the 1 cm mark. Do not close your fingers around the ruler. Have your friend randomly decide when to drop the ruler. As fast as you can, close your fingers.

At what cm mark did you close your fingers?
Switch places with your friend and compare your reaction times!

For an added challenge, test your auditory reaction time. Set up the experiment the same way but close your eyes. Have your friend make a sound when he drops the ruler. Were you faster or slower?

IMAGES CREATED BY GAVS