Calculating and Graphing Speed

09.10.12

Warm-up

What is the mathematical equation for calculating average speed?

Objective

• I can calculate average speed.

Speed v. Velocity

• Speed is the amount of distance covered over a given time.– Example: the car is going 80 mph

• Velocity is the speed and direction an object is traveling.– Example: the car is traveling North at 80 mph

Calculating average speed

• Average speed (v) = total distance (d)/total time (t)• v = d/t• t = d/v• d = vt

Units for speed or velocity

• distance per unit of time– mph (miles per hour)– km/h (kilometers per hour)– ft/sec (feet per second)– m/s (meters per second)– nm/ms (nanometers per millisecond)

Quick practiceTotal distance Total time Average speed Units for ?

a. 45 km 1.5 h ?b. 26 m ? 13 m/sc. ? 1.75 s 21.2 m/s

Practice problems1. (easy) Your family drove 55 miles to downtown Denver in

0.75 hours. What was your average speed?

2. (moderate) If a plane travels 2190 km at 330 km/h, how long is the flight?

3. (difficult) Mr. Founds’s friend completed an Ironman yesterday. Her average speeds and times for each leg are listed below. Calculate the distance for each leg of the event. Swim 328 feet/minute 1.5 hours

Bike 15.31 mph 7.33 hours

Run 12.9 minutes/mile 4.5 hours

Practice ProblemsDistance Time Speed Units

a. 50 miles 2 hours ? ?b. 45 miles 1.5 hours ? ?c. 18 meters 5 seconds ? ?d. 90 feet 2 days ? ?e.* 1250 km ? 500

km/h?

Assignment

• Page 11 (#5,7,9,10)

DOL

• If an object travels 113 meters in 10 seconds, what is the average speed of the object?

• What is the difference between speed and velocity?

Objective

• I can create and analyze motion graphs

Warm-up

• A bus averages 19 miles per hour taking you to school using a 5 mile route.

• You can ride your bike to school in 15 minutes using a 3 mile route.

• Which is faster? • What is your average speed riding your bike?

Hint: You need to convert 15 minutes into hours

Graphing motion

• Distance-time• Speed-time– Line graphs– Time on x-axis– Used to analyze the motion of an object

Distance-Time• Time on x-axis• Distance on y-axis• Linear data

– Constant speed

• Nonlinear data– Acceleration

• Positive slope– Object moving away form starting

point

• Negative slope– Object returning toward starting

point

• No slope– Object stationary

• Steeper slope– faster average speed

• Slope of line = average speed

DOL

• Calculate average speed of ball• Describe motion of ball.

Warm-up• Position is the same as distance

1. Describe the motion of each object.

2. Which object is moving faster, B or D?

3. Why does object A have a negative slope?

Story time – Graph it!• Jan heads out on her bike at noon and rides 10 miles on the

bike path in one hour.• She stops for 30 minutes to update her Facebook status and

drink a Monster.• Feeling invigorated by the rush of likes and processed

chemicals she decides to continue riding up to her friends house which is another five miles away. She rides this distance in 30 minutes.

• She spends 2 hours at her friends house listening to Justin Bieber, playing Call of Duty: Modern Warfare 3, and eating Takis.

• With the effects of the Monster worn off and sprinkles of processed cheese dust adorning her face and clothing, Jan then makes the long trek home taking 4 hours to get home.

Speed-Time• Time on x-axis• Speed on y-axis• Linear, positive

– Constant, positive acceleration

• Linear, negative– Constant, negative

acceleration• Nonlinear, positive

– Increasing positive acceleration

• Nonlinear, negative– Increasing negative

acceleration• No slope

– Constant speed

Lidar (article)

• How does lidar detect speed?

Assignment

• Page 19 (#1-6)

DOL

1. What type of graph is shown?

2. How would you describe the motion of the object?

3. Sketch a speed-time graph that would show this data.

Time Position

0 0

0.4 100

0.8 400

Uintah and El Paso traffic analysis

• Testable Question– What is the average speed of vehicles near the intersection of

Uintah and El Paso?• Procedure– Calculate the average speed of vehicles for these four areas:

• Row 1 - traveling westbound on Uintah before El Paso intersection• Row 2 - traveling westbound on Uintah after El Paso intersection• Row 3 - traveling eastbound on Uintah before El Paso intersection• Row 4 - traveling eastbound on Uintah after El Paso intersection

– If traffic light turns red during data collection, data will be discarded.

Warm-up

• If a car travels 264 feet in 4.9 seconds, what is the average speed of the car in miles per hour?– Hint: calculate speed in feet per second and then

multiply your answer by 3600 and then divide that answer by 5280.

– Use a calculator if you have one.– If you don’t have a calculator set up the problem

but don’t solve it.

Learning Target

• I can analyze and interpret experimental data.

Speed Trap Investigation

Analyzing Data

1. Drop the lowest and highest times from each set of data.

2. Determine the median of each set of data.

3. Calculate the speed using the median time and convert to miles per hour.

a) 264/median timeb) Multiply by 3600c) Divide by 5280

4. Create bar graph showing median speed for each speed trap for each class period.

Interpreting data

Typically a 10% percent difference or more is considered significant.1. Is there a significant difference

between the four speed traps? Attempt to explain why or why not.

2. Is there a significant difference between the class periods? Attempt to explain why or why not?

3. What are some potential sources of error in the investigation and what improvements could be made?

Speed Trap Investigation• Testable Question– What is the average speed of vehicles traveling on

Uintah near El Paso?• IV – speed traps

• DV – speed of vehicles

• Procedure– Time 10 cars in speed trap– Determine median time– Calculate speed

Row 1

Row 3Row 2

Row 4