Unit #2 Math and Your Car

Unit #2 Math and Your Car Name Date Period ~ 0 ~

Choosing your Cars To start this unit, you are going to choose three cars online. You will be using these cars to investigate car loans and calculate the cost of a trip. Note the restrictions in step 4. You want your cars to have different prices and mpg according to 1) Go to www.carprices.com. 2) Choose the manufacturer of the car you would like to purchase. 3) Choose from the different car models for that manufacturer. 4) Restrictions for choosing cars: a. The car must have the mpg listed or you must find it somewhere else online. You could use a different website or a search engine to do so. b. Each of the cars must have a difference of i. at least $3,000 in price (ex: $16,000 and $19,000). ii. at least 5 mpg in highway gas mileage (ex: 25mpg and 30 mpg). c. At least one car must have a reasonable price (under $30,000). 5) Record the name of the car, the base (lowest) price, and the city and highway miles per gallon in the table below. 6) Repeat the process to find two more options for your car. Name and Year Car #1 Car #2 Car #3 Base Price City MPG Highway MPG ~ 1 ~

Car Loans Deciding what type of car to buy is a big decision. Unless you can pay cash for the car, the decision can be made for you by how much you can afford to pay each month. If you borrow the money, the amount you pay each month depends on how much you borrow, for how long, and the interest rate. When making your decision, you also want to consider the total cost of the car after you are done making the payments. 1) First, copy down the car names and prices from the activity we did in the computer lab into table A on the next page. You will be considering a 3-year loan (36 months) with 6.25% interest. 2) You will be using the financial application called the TVM solver on the graphing calculator to find the monthly payments. a. APPS #1 #1 i. The screen should look like this. b. Write what each abbreviation stands for: N= I%= PV= PMT= FV= P/Y= C/Y= c. The number of payments (N) will be. d. I% will be. e. Leave a 0 in payment (PMT) because that is what we will find. f. The present value (PV) is the amount you owe or the cost of the first car. g. The future value (FV) is the amount you hope to owe at the end which is $0. h. P/Y and C/Y should always be 12! i. The screen should now read N= 36 I%= 6.25 PV= your car cost PMT= 0 FV= 0 P/Y= 12 C/Y= 12 Clearing your Calculator: This is a good idea whenever you use the calculator after someone else, especially if they have used the APPS or STAT menu. 2nd + 7 1 2 Your calculator should indicate that the RAM has been cleared. ~ 2 ~

j. Bring the cursor back up to PMT. k. Press ALPHA then ENTER. 3) This amount is your monthly payment. Write this amount in table A. 4) Multiply this number by the months you will be paying it, 36, to find the total cost. 5) Find the difference between the total cost and the base price. 6) Find the percent increase in the cost from the loan by dividing the difference by the total cost. 7) Repeat the Process for Cars 2 and 3. Just change the PV in the TVM solver to the cost of that car and solve for the payment again. Name and Year TABLE A Car #1 Car #2 Car #3 Base Price Monthly Payment Total Cost Difference Total Cost Base Price Percent Inc. Compare each of your cars: 1. How did the base price of the car impact the monthly payment? 2. How did the base price of the car impact the difference between the total cost and base price? 3. How did the base price of the car impact the percent increase in the cost? ~ 3 ~

You will now be considering a 5 year loan with the same interest rate of 6.25%. This will be months or payments. Copy the name and base price of your three cars from the previous page in table B. USE THE DIRECTIONS ON THE PREVIOUS PAGES TO: Use the TVM solver to find the monthly payments. Calculate the total cost, difference in price, and percent increase. Name and Year TABLE B Car #1 Car #2 Car #3 Base Price Monthly Payment Total Cost Difference (Total Cost Base Price) Percent Inc. Compare your first car in Table B with your first car in Table A. 1. How did the length of the loan impact the monthly payment? 2. How did the length of the loan impact the difference between the total cost and base price? 3. How did the length of the loan impact the percent increase in the cost? 4. What is a reason you might choose the first loan? 5. What is a reason you might choose the second loan? ~ 4 ~

You will now be considering a 5 year loan with a lower interest rate of 5.0%. This will still be months or payments. Copy the name and base price of your three cars from the previous page in Table C. USE THE DIRECTIONS ON THE FIRST PAGES TO: Use the TVM solver to find the monthly payments. Calculate the total cost, difference in price, and percent increase. Name and Year TABLE C Car #1 Car #2 Car #3 Base Price Monthly Payment Total Cost Difference (Total Cost Base Price) Percent Inc. Compare your first car in Table C with your first car in Table B. 1. How did the interest rate impact the monthly payment? 2. How did the interest rate impact the difference between the total cost and base price? 3. How did the interest rate impact the percent increase in the cost? 4. Which loan would you choose? 5. In general, describe the type of loan you would look for when buying a car? ~ 5 ~

Miles Per Gallon Gas mileage is a very important factor to consider when buying a car. Miles per gallon (mpg) is the rate of how many miles the car can travel on one gallon of gas. You do not need to burn exactly 1 gallon of gas to calculate your car s mpg. Instead, fill your car s gas tank completely, reset the odometer, and drive around on your typical route for a couple of days. When you refill your car s tank with gas, use the odometer to figure out how many miles you have driven and the gas receipt to find out how many gallons of gas your car has used. Divide the number of miles driven by the number of gallons your car has used. This will be your gas mileage or miles per gallon (mpg). Formula for Miles Per Gallon (mpg) The following different real life situations involving gas mileage. 1. Julian has had his car for a couple of years, and he knows it gets better than average gas mileage. On a recent trip to an amusement park, he used 14 gallons of gas and drove 471 miles. To the nearest tenth, what is his gas mileage? 2. Chris loves to watch NASCAR racing. He finds out that his favorite driver burns 106 gallons of gas in a 600 mile race. Calculate the miles per gallon for the stock car to the nearest tenth. Why do you think his gas mileage is so low? 3. Marilea has a new Sportage. On a recent trip to the Jersey Shore she drove 225 miles and used 8.2 gallons of gas. What was her gas mileage? 4. Jason has a 15 gallon gas tank in his car. If his car gets 22 miles to the gallon, how far can he drive on a tank of gas> 5. Roy bought a new car that is supposed to get on average 28 miles to the gallon. Roy fills up his gas tank, drives 325 miles, and fills up his tank again. To refill his tank he needed 13 gallons of gas. What is his gas mileage? Did his car perform as well as advertised? 6. Hank is taking 445 mile trip. His car s gas tank holds 20 gallons of gas and gets 23 miles to the gallon. Can Hank take the trip on without refilling his gas tank? ~ 6 ~

Fill Er Up Task In this activity, you will choose where you are going on a vacation and calculate the cost of gas to drive there and back. You will compare the difference between that cost ten years ago and what you have to pay today. Your vacation destination must be: 1. Outside of New York or any state that borders New York. 2. Accessible by car (i. e. not Hawaii). Process Your Cars a) In columns A and B in the table on the next page, record the names of the three cars and their highway MPG. We are using highway MPG because you usually travel on major high speed roads for long trips. Researching the Trip a) Go to Mapquest (www.mapquest.com). b) Type your home address in the Start section. c) Type the destination for your vacation in the End section. d) If you want to go to a place, but do not know the address for it, you can go to www.google.com and type the word address and where you want to go. e) After entering the information into mapquest, press GET DIRECTIONS. f) Record the total miles for the trip (one-way). g) Multiply this number by two to find the total traveling distance. Record this number in column C for each of the three cars. Finding the Cost Now that you have found the length and type of driving required for the trip, you need to calculate the cost of the gas for the trip now and ten years ago. a) The price of gas ten years ago was $1.66 per gallon (adjusted for inflation). Write this value in the first cell in column E. b) The price of gas today is per gallon. (Find this value by searching online). Write this value in the first cell in column F. c) Complete the Chart for each of your three car choices. Use the Method row to help you if you are not sure how perform the calculations. d) Answer the reflection questions at the end of the activity. ~ 7 ~

(Round to the nearest hundredth.) Car Method A. B. C. D. E. F. G. H. MPG HWY Miles ----- ----- miles mpg Total Gallons of Gas Cost of Trip Ten Years Ago: rate gallons Cost of Trip Today: rate gallons Difference Between E and F Cost Today - Cost 10 years ago Percent increase change in cost original cost 10 years ago 100 Car #1 Car #2 Car #3 ~ 8 ~

Reflection Questions 1. Was the total cost of the trip today more or less than you expected? By how much? 2. Compare your two cars with the biggest average difference between their mpg for highway driving. What is the difference between their today costs for the trip? 3. Is this more or less than you would expect? 4. How many miles do you think you would drive in a year? (The average is 15,000, so choose a number between 10,000 and 20,000.) 5. Using the number of miles you drive in a year, how much more would the car with the worst gas mileage cost than the one with the best mileage? Use today s cost of per gallon. Formula: miles price per gallon mpg 6. What do you notice about the percent increase (column H) for the cost of the trip for the three car choices. Why did this happen? ~ 9 ~

Car Insurance Vocabulary: Liability Coverage: Collision Coverage: Comprehensive Coverage: Deductible: Premium: Car Insurance Tips: Increasing your deductible usually lowers your premium. If you are willing to pay more out of pocket when you get in an accident, you will pay less each year for having the insurance. Eliminate optional coverages (e.g., towing and labor, rental insurance) from your auto insurance. Consider dropping collision and/or comprehensive coverages on older cars. If your car is worth less than 10 times the premium, purchasing the coverage may not be worth it. Ask about available discounts for your auto insurance (airbags, drivers education, defensive driving, low-mileage discounts, discounts for safety or antitheft devices). Avoid buying a vehicle that is more likely to be vandalized. Choose a car with a low cost to replace parts. Keep your car in a garage. Drive safely to establish a good driving record. If you have had tickets or accidents that were your fault in the past three years your premium will be higher. ~ 10 ~

Cost of Car Insurance: 1) You have car insurance with a $600 premium every six months and a $500 deductible. How much would you pay in a six month period if you had an accident that that was your fault and cost $150 to repair? 2) You have car insurance with a $450 premium every year and a $800 deductible. How much would you pay in the six month period if you did not have an accident? 3) You have car insurance with a $800 premium every six months and a $300 deductible. How much would you pay in the six month period if you had an accident that was your fault and cost $1000 to repair? 4) You have car insurance with a $120 premium every month and a $500 deductible. How much would you pay in the six month period if you had an accident that cost $3000 to repair? 5) You have car insurance with a $300 premium every six months and a $1500 deductible. How much would you pay in the six month period if you had an accident that that was your fault cost $2000 to repair? 6) You have car insurance with a $700 premium every year and a $1500 deductible. How much would you pay in the six month period if you had an accident that that was your fault cost $200 to repair? ~ 11 ~

Yearly Cost of Owning a Car The information for the following activity was taken from www.aaaexchange.com. Every Year AAA does an extensive study on the cost of car ownership. They categorize the costs into operating costs (fuel, maintenance, and tires) which are dependent on the number of miles you drive and ownership costs (insurance, license/registration/taxes, depreciation based on 15,000 miles, and finance charge) that are calculated per year. We will study their findings for small sedans and SUV s in 2011. They also conduct their studies for medium sedans, large sedans, and minivans. Complete the two tables below. 1. Find the total cost per mile. 2. Use the number of miles you think you drive in a year to calculate the total operating cost. 3. Find the total ownership cost per year. 4. Add the operating costs to the total ownership cost to find the total yearly costs. Small Sedan Operating Costs Per Mile Ownership Costs Per Year Fuel 10.05 cents Full Insurance Coverage $951 Maintenance 4.11 cents License, Registration, Taxes $438 Tires.67 cents Depreciation (averaged over 5 $2,560 years, based on 15,000 miles) Total Cost Per Mile Finance Charge (interest from a loan or lease) $584 Total Operating cost for miles Total Ownership Cost Per Year Total Yearly Cost for the small sedan: SUV Operating Costs Per Mile Ownership Costs Per Year Fuel 17.04 cents Full Insurance Coverage $912 Maintenance 4.80 cents License, Registration, Taxes $757 Tires 1.14 cents Depreciation (averaged over 5 $5,052 years, based on 15,000 miles) Total Cost Per Mile Finance Charge (interest from a loan or lease) $1,071 Total cost for miles Total Ownership Cost Per Year Total Yearly Cost for the SUV: ~ 12 ~

Minimizing your Costs 1. Fuel: Base on the late 2010 rate of $2.880 per gallon. a. Is the gas price higher or lower now? b. Why is the SUV price for gas so much higher than the small sedan? c. List two ways you can decrease the yearly price of gas. 2. Maintenance: Includes the cost for parts and labor for routine maintenance as well as an average amount of wear and tear. Sales taxes are included. It is difficult to control the maintenance cost for your car. You can make sure that your car gets regular maintenance such as oil changes so that you will not have costly repairs later. 3. Tires: Based on the price of tires at the recommended number of miles that are identical to the tires that came with the car. It is difficult lower the tire cost because cheaper tires might not last as long. 4. Insurance: Based on a married 47-year-old male with a good driving record, living in a small city. The policy gives average coverage with a $500 deductible for collision and a $100 deductible for comprehensive coverage. a. Do you think your car insurance would cost more or less than the amount listed here? 5. License/Registration/Taxes: Includes all government taxes and fees when purchasing the car and fees due each year to license and register the car. You do not have much control over these costs. If you buy a cheaper car, however, the initial taxes will not be as high. ~ 13 ~

6. Depreciation: Based on the difference between a new-vehicle purchase price and the estimated trade-in value at the end of five years. a. How could you decrease the amount of depreciation on your car? Think about the type of car you buy. 7. Finance Charge: The finance charge is based on a five-year loan at 6% interest with a 10% down payment. Taxes and first year license fees are included. a. How you could decrease or even eliminate the finance charge? Yearly Cost for YOUR car Using the values in the two tables at the beginning of the activity as well as your answers to the minimizing the cost questions, calculate how much it would cost for you to maintain a car you might have now or in the future. Make this as realistic as possible. For example, if you know you would need a car loan, do not cut out the finance charge. Operating Costs Per Mile Ownership Costs Per Year Fuel Full Insurance Coverage Maintenance License, Registration, Taxes Tires Depreciation (averaged over 5 years, based on 15,000 miles) Total Cost Per Mile Finance Charge (interest from a loan or lease) Total Operating cost for miles Total Ownership Cost Per Year Total Yearly Cost for YOUR car: ~ 14 ~

Rating Car Traits When purchasing a car, what features matter the most? A recent survey of different age groups was conducted to answer that question. The choices for the survey were appearance, cost, safety rating, and make of the car. The results are shown below in an augmented bar graph. The numbers on the y-axis are percents. 100 90 80 70 60 50 40 30 20 10 0 Visual Appeal Safety Cost Make Age 50+ Age 25-49 Age 16-24 1. Which feature was most common among all respondents? 2. Which feature was the most common in the 16-25 age group? What percent of the people in that age group chose that feature? 3. Which feature was the most common in the 50+ age group. What percent of the people in that age group chose that feature? 4. As the age of the respondents increased, which feature became less important? Why do you think this happened? 5. One feature of an augmented bar graph is the diagonal lines drawn between the columns. How do these lines enhance the graph? ~ 15 ~

Conduct Your Own Car Traits Survey As a class we collected data for what you thought was the most important quality when choosing a car. Instead of using age groups we collected the information for boys and girls. Organize the result in this table. Round to the nearest whole number. Gender Total in Visual Safety Cost Make Class Appeal Boys: numbers Boys: % of total Girls: numbers Girls: % of total Create an augmented bar graph of the data we collected. Answer the following questions. Make sure that you would get the same answers from your table as your graph. This is a good way to make sure your graph is constructed correctly. 1) Which of the four responses was the most/least common among all respondents? Most: Least: 2) Which of the four responses was the most/least common among the boys? Most: Least: 3) Which of the four responses was the most/least common among the girls? Most: Least: 4) How do the opinions of your class compare to the opinions of the 16-24 year old age group on page 14? Were the boys or the girls in your class more similar to them? ~ 16 ~

How Long Does it Take to Get There? 1) Write half an hour as a decimal. What does half an hour mean? 2) Write three and one quarter hours in hours and minutes and as a decimal. 3) Write five and thirty-seven sixtieths of an hour in hours and minutes and as a decimal to the nearest hundredth. 4) Convert 4 hours 27 minutes to a decimal. D=RT 5) You are driving 230 miles at a speed of 45 miles per hour. How long does it take you to make the trip? Round to the nearest minute. (Do this problem in the textbox to the right.) Once you find the time, you can convert the decimal to minutes by multiplying it by 60. hours hours minutes 6) You are driving 230 miles at a speed of 60 miles per hour. How long does it take you to make the trip? Round to the nearest minute. 7) How much time would you save if you went 60 mph on this trip instead of 45 miles per hour? ~ 17 ~

How much time are you saving? In each problem, round to the nearest minute. Sometimes it is tempting to go faster than the speed limit to save time when driving long distances. Today we are going to find out how much time you are really saving. Let s assume that the speed limit is 65 mph. We will compare this with traveling at 75 mph. 1) Traveling from Saugerties to Albany, NY. Distance: 45 miles. a. Time when traveling at 65 mph: b. Time when traveling at 75 mph: c. Time Saved: 2) Traveling from Saugerties to Seaside Heights, NJ. Distance: 187 miles. a. Time when traveling at 65 mph: b. Time when traveling at 75 mph: c. Time Saved: 3) Traveling from Saugerties to Washington D.C. Distance: 328 miles. a. Time when traveling at 65 mph: b. Time when traveling at 75 mph: c. Time Saved: How will this lesson impact the speed at which you drive? ~ 18 ~

D=RT Multistep Problems It is an important life skill to be able to calculate the amount of time it will take you to get somewhere. In order to do so, you just need to know the distance to your location and the average speed at which you will travel. You can also use the formula, distance=rate(time) to determine your total distance travelled when you know your speed and the amount of time you have been travelling. Lastly, you can calculate the speed at which you travel when given the travel time and the total distance. Answer the questions below. 1. Jessica needs to travel 240 miles. To start out, she drove for 2 hours at 45 miles per hour. After stopping for a lunch break, she finished the trip travelling at 50 miles per hour. How long did she drive in the second portion of her trip? 2. You drove for 3 hours at 45 miles per hour. After stopping to buy some souvenirs in a famous town along the way, you drove for 2 more hours at 65 miles per hour. After eating a quick dinner at a rest stop, you finished your driving with 2 more hours at 65 miles per hour. What was the total distance you travelled? 3. Jerome needs to travel 305 miles to get to Myrtle Beach. In the first three hours he was able to travel at 65 miles per hour. For the last two hours there was more traffic. On average, how fast did he travel for these last two hours? 4. Louis is going on a 265-mile trip. To start out, he drove for 2 hours at 65 miles per hour. After stopping to get gas, he finished the trip travelling at an average of 45 miles per hour due to traffic. How long did the second portion of the trip take? ~ 19 ~

5. Justin drove for 3 hours at 45 miles per hour. For the next two hours, Justin travelled on a major highway at 60 miles per hour. After eating a leisurely dinner with some friends who lived along the way, he finished driving 2 more hours at 55 miles per hour. What was his total distance travelled? 6. I need to travel 345 miles to get to a wedding. For the first three hours, I travelled at 60 miles per hour. If I need to arrive at my destination in another three hours, how fast should I drive for the remainder of my trip? 7. A group of friends are taking a 315-mile road trip. To start out, they drove for 3 hours at 60 miles per hour when they got a flat tire. After replacing the flat with a donut, they finished the trip at 45 miles per hour for obvious reasons. How long did the second portion of the trip take? 8. Lucinda drove for 3 hours at 60 miles per hour. For the next three hours, she travelled in stop and go traffic, averaging 45 miles per hour. After stopping to take pictures of some historical landmarks on the way, she finished her trip with 3 more hours at 60 miles per hour. What was her total distance travelled? 9. Make up your own question that is similar to one of the questions in this lesson. Make it applicable to a trip you would actually take in your life. Q: A: ~ 20 ~

Drunk Driving There are always risks when driving a car, but there are certain times of day when these risks are higher due to drunk driving. Complete the table below and answer the related questions to learn more about when it is most dangerous to be on the road. For each time interval, calculate the percent of the fatal crashes that were alcohol related. Round to the nearest percent. If necessary, use scrap paper to perform your calculations. Time of Day in 3 hour intervals Total Number of Fatal Crashes Number of Alcohol related fatal crashes Midnight - 3:00 AM 4725 3716 3:00AM 6:00 AM 2767 1751 6:00 AM - 9:00 AM 3545 510 9:00 AM - 12:00 PM (noon) 3620 404 12:00 PM - 3:00 PM 4749 752 3:00 PM - 6:00 PM 6301 1639 6:00 PM - 9:00 PM 5873 2790 9:00 PM - Midnight 5447 3474 Percent of Fatal Crashes that were Alcohol Related Note: This data was taken from the Highway Safety Administration in 1996. They no longer publish this data in 3 hour intervals. Currently there are less total traffic fatalities due to improved safety features, but the percentage of alcohol related fatal crashes for each time of day remains consistent. 1. On the next page, draw a histogram showing the relationship between the time of day and the percent of fatal crashes that involve alcohol. 2. During what time of day is a fatal accident most likely to involve alcohol? Why do you think this is true? 3. There is a law for young drivers that relates to this activity. What is this law? 4. The highest number of fatal accidents occur between 3:00 PM and 6:00 PM. Why do you think this is true? 5. Even though there are so many fatal accidents at this time, if you are driving, why is your probability of getting in a fatal accident still greater at night? ~ 21 ~

Draw the histogram for the drunk driving activity here. ~ 22 ~

Buckle Up According to the Highway Safety Administration, 83% of the people in our nation wear seat belts. In the first two columns of the table below are the ages and number of people who died in 2009 in car crashes when they were wearing a seatbelt (or using a car seat). To do the activity below, we will start by assuming that wearing a seat belt does not really make a difference. Calculate the expected number of people that would die in a car crash when they are not wearing any restraint based on the fact that 83% of people wear a seatbelt and 17% do not. Use the example proportion for your calculations. The fourth column lists the actual number of people that died in 2009 in car crashes when they are not wearing seatbelts. In the last column, find the difference bewteen the expected number of fatalities (column 3) and the actual number of fatalities (column 4) when not wearing a seat belt. This difference is the number of people who die because they did not wear use a restraint. The method for this process is shown in the first row. Age Car Crash Fatalities with a restraint (seat belt or car seat) Expected Number of car crash fatalities with no restraint Actual Number of car crash fatalities with no restraint Difference, or number of people who die because they did not use a restraint 0-3 153 74 74-31=43 4-7 119 78 43 people 8-12 110 115 13-15 104 238 16-20 1360 2014 21-24 946 1727 25-34 1402 2674 ~ 23 ~

35-44 1157 1898 45-54 1349 1703 55-64 1285 1023 65-74 1057 606 75+ 1592 700 Totals 10,642 12,865 Note: This data was taken from the Highway Safety Administration in 2009. The totals include other fatalities where the age was unknown. According to this activity, how many people die each year because they do not wear a seat belt? Only you know if you always buckle up. Hopefully this activity has convinced you of the importance of doing so. ~ 24 ~

Reaction Time The last area of car safety we will be studying is following distance. Following distance is important for two reasons. First, it takes every driver time to react when in a potentially dangerous driving situation. During this time, your car is still traveling forward. Second, once a driver decides to apply the brake, it takes the car time (and therefore distance) to stop. In this activity, we will be doing an experiment about the first factor in following distance, reaction time. Follow the steps below. a) Work in pairs with one partner is seated and one partner standing. b) The standing partner should be behind the seated partner, dangling a ruler in front of the seated partner. The ruler should be held so that the seated partner can see the ruler but not the hand of the standing partner. c) The seated partner will hold their hand up so that his/her thumb and index finger are opened at the one inch mark on the ruler. d) At a random moment, the standing partner will let go of the ruler. e) The seated partner will pinch his or her fingers closed around the ruler as soon as they realize it is dropping. f) Subtract one inch from the number of inches where the student caught the ruler because the fingers started at the one inch mark. For example, if the seated student caught the ruler at the seven-inch mark, the ruler dropped six inches while he/she was reacting. g) The seated partner should record the data in the inches column of the table on this page. h) Repeat this process for a total of 15 trials. i) Switch positions (seated or standing) and repeat the experiment for the new seated partner. Trial Change of Position Trial Change of Position Trial Change of Position 1 6 11 2 7 12 3 8 13 4 9 14 5 10 15 1. Calculate the average change of position for the fifteen trials. Round to the nearest tenth of an inch. 2. Use the formula,, where t is reaction time in seconds and d is the average change of position in inches to calculate your reaction time. Round to the nearest thousandth of a second. 3. Do you think it would take more or less time to react while driving a car? Why? ~ 25 ~

Conversion notes for the 2-Second Rule Activity Round all values to the nearest tenth. a) Method for converting from miles into feet: b) Method for converting from hours into minutes: c) Method for converting from minutes into seconds: d) The method for converting from Miles per Hour into Feet per Second: e) How could we simplify this? Ex) Ex) Convert 47 miles per hour into feet per second. Convert 72 miles per hour into feet per second. Why would this conversion be necessary when we are finding stopping distance? Converting from Miles per Hour into Feet per Second: ~ 26 ~

Two Second Rule Round Answers to the nearest tenth! Introduction If you have taken driver s education class before, or if you already have your license, you have probably heard of the 2-second rule. The 2-second rule simply means that you should leave a 2- second gap between your car and the car in front of you when you are driving so you do not hit it if it stops suddenly. Is 2 seconds enough time? Could it be okay for certain speeds and not for others? Today we will answer that question using math. A. We will calculate how much space is between you and the car in front of you if you maintain a 2, 3, 4, or 5 second following distance at different speeds. B. We will then compare this distance to how far you travel, on average, as you react and stop your car. If the distance between you and the car in front of you is larger than your stopping distance, you are safe. If not, you have just been in an accident that is your fault! Distance Between Cars For this part of the activity, you will be calculating the feet between your car and the one in front of you at speeds between 10 mph and 70 mph in intervals of 10mph. 1) First, miles per hour is not a very useful measurement because we are looking for how many feet you travel in 2-seconds. Therefore, we must convert miles per hour into feet per second. You learned how to do this on the previous page. 2) In Table A, record the feet per second conversion. (Row 2) 3) If that is how many feet the car travels in a second, multiply it by 2 to get the two second following distance. (Row 3) 4) For future use, calculate a 3, 4, and 5 second following distance by multiplying the feet per second conversion by the number of seconds. (Rows 4-6) Table A 1 Speed mph 10 20 30 40 50 60 70 2 Speed fps 3 2 sec. distance 4 3 sec. distance 5 4 sec. distance 6 5 sec. distance ~ 27 ~

Reaction, Braking, and Total Stopping Distance Dry Roads There are two time intervals that take place when you stop your car. The first is the time it takes you to react and realize you need to stop and the other is the time it takes your car to stop once you start braking. 1) Once again, it will be more helpful to have the speeds in feet per second. Therefore, copy feet per second conversions from Table A to Table B. 2) If a person is paying attention, it takes them about.67 seconds to react and begin braking in a potentially dangerous situation. (If they are on a cell phone, daydreaming, tired, or drunk, it will take much longer.) In row three, calculate how far a person travels at each speed in.67 seconds. ( ). 3) In row four, some of the braking distances from actual tests are recorded. Find the pattern to fill in the braking distances for 50 mph, 60 mph, and 70 mph. 4) Add the reaction distance and brake distance to find the stopping distance. (Row 5) 5) Compare your total stopping distance with the 2 second, 3 second, 4 second, and 5 second following distances in Table A. In the sixth row of Table B, suggest a following distance for that speed. Your choices are 2 seconds, 3 seconds, 4 seconds, 5 seconds. Table B 1 Speed - mph 10 20 30 40 50 60 70 2 Speed - fps 3 Reaction Distance 4 Braking Distance 5 Stopping Distance 20 45 80 125 6 Suggested Following Distance: 2, 3, 4, 5, or more seconds ~ 28 ~

Reaction, Braking, and Total Stopping Distance Wet Roads This section is similar to the last, but now we are dealing with wet roads which significantly increase your braking distance. 1) Once again, it will be more helpful to have the speeds in feet per second. Therefore, copy feet per second conversions from Table A to Table C. 2) If a person is paying attention, it takes them about.67 seconds to react and begin braking in a potentially dangerous situation. (If they are on a cell phone, daydreaming, tired, or drunk, it will take much longer.) In row three, calculate how far a person travels at each speed in.67 seconds. ( ). 3) In row four, some of the braking distances from actual tests are recorded. Notice they are much longer than the braking distances on a dry road. Find the pattern to fill in the braking distances for 50 mph, 60 mph, and 70 mph. 4) Add the reaction distance and brake distance to find the stopping distance. (Row 5) 5) Compare your total stopping distance with the 2 second, 3 second, 4 second, and 5 second following distances in Table A. In the sixth row of Table B, suggest a following distance for that speed. Your choices are 2 seconds, 3 seconds, 4 seconds, 5 seconds. Table C 1 Speed (mph) 10 20 30 40 50 60 70 2 Speed (fps) 3 Reaction Distance 4 Braking Distance 40 90 160 250 5 Stopping Distance 6 Suggested Following Distance: 2, 3, 4, 5, or more seconds ~ 29 ~

Graph of 2-second Rule Activity: On the following table, use Speed in MPH as your independent variable (x). Use an appropriate scale for 0 mph to 80 mph. Use Distance in Feet as your dependent variable (y). Use an appropriate scale for 0 feet to 800 feet. Make the following line graphs: A. Graph 2: Speed vs. Stopping Distance on Dry ground (Table B: Rows 1 and 5) B. Graph 3: Speed vs. Stopping Distance on Wet Ground (Table C: Rows 1 and 5) 1) Do the graphs form straight lines? Which is more curved? 2) What do you think should be the maximum speed for driving on wet roads? 3) What advice would you give to young drivers like yourself? 4) In this activity we are assuming that the car in front of you comes to a complete stop immediately. This would happen if that car hit something without applying the brakes to give you warning. The person driving the car could also slam on their brakes and come to a complete stop or a partial stop. This would give you some more time, but you still want to prepare for the worst case scenario. What situations can you think of where the car in front of you might hit something without having time to apply the brakes? ~ 30 ~