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**Speed and Velocity Speed and Velocity**

What is speed, velocity and acceleration? Speed and Velocity (Use with Speed, Velocity and Acceleration handout)

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**Distance: meters (m), miles (mi) **

Speed is the distance traveled per unit of time. Speed (s) = distance (d) time (t) Each variable measured by units: Distance: meters (m), miles (mi) Time:seconds (s), hours (hr), minutes (min) Speed: meters per second (m/s), miles per hour (mi/hr), kilometers per hour (km/hr)

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**Instantaneous, Average, Constant**

3 TYPES OF SPEED Instantaneous, Average, Constant Pretend you are looking at your car's speedometer while you are driving. The reading you get from your speedometer is A. instantaneous speed… This is the speed that you are traveling at that moment.

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**B. Constant Speed is when the object covers equal distances in equal amounts of time.**

C. Average speed is the total distance traveled divided by the total time. It can be calculated using the following formula: speed = distance time Average Speed is: Total distance = all distance traveled over Total time = final time (end) minus initial time (beginning) ...or shortened:

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**Four Step Approach to Solving Problems G.U.E.S.S.A.**

Step 1 READ THE PROBLEM. Draw a picture. Step 2 IDENTIFY THE VARIABLES Write down what you know. GIVEN What are you trying to find? UNKNOWN Step 3 WRITE FORMULA EQUATION Set up the formula. (The formula should match the unknown.) Step 4 PLUG IN THE NUMBERS SUBSTITUTE DO THE MATH SOLVE. Check ANSWER with UNITS

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**“A car traveled 110 miles in 2 hours.”**

Consider the problem… “A car traveled 110 miles in 2 hours.” Step 1 Read the problem. Draw a picture. 110 miles 2 hours Formula Plug-in Answer d = t = s = Units, units, units!

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**? “A car traveled 110 miles in 2 hours.” 110 miles 2 hours Formula**

Step 2 Write down what you know. GIVEN What are you trying to find? UNKNOWN 110 miles 2 hours Formula Plug-in Answer d = 110 miles t = 2 hours s = ? Units, units, units!

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**FORMULA SHOULD MATCH THE UNKNOWN**

“A car traveled 110 miles in 2 hours.” Step 3 Set up the formula. FORMULA SHOULD MATCH THE UNKNOWN s = d t Formula Plug-in Answer d = 110 miles t = 2 hours s = ? Units, units, units!

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**? “A car traveled 110 miles in 2 hours.” Formula Plug-in Answer d =**

Step 3 Set up the formula. EQUATION Formula Plug-in Answer d = 110 miles t = 2 hours d S = s = ? t Units, units, units!

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**“A car traveled 110 miles in 2 hours.”**

Step 4 Plug-in the numbers. SUBSTITUTE AND SOLVE. CHECK UNITS 55 mi/hr Formula Plug-in Answer d = 110 mi 2 hours t = d 110 mi S = S = S = 55 mi/hr s = 55 mi/hr t 2 hr Units, units, units!

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**Do the problems 1-3 on your notes.**

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**CIRCLE AND LABEL INFO PROVIDED!**

Consider the problem… “A runner’s average speed during the 10 kilometer race was 20 km/hr. What was his time?’” Step 1 Read the problem. Draw a picture. CIRCLE AND LABEL INFO PROVIDED! Speed of runner: 20 km/hr 10 km Formula Plug-in Answer d = t = s = Units, units, units!

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**“A runner’s average speed during the 10 kilometer race was 20 km/hr**

“A runner’s average speed during the 10 kilometer race was 20 km/hr. What was his time?” Step 2 Write down what you know. GIVEN What are you trying to find? UNKNOWN Speed of runner: 20 km/hr 10 km Formula Plug-in Answer d = 10 km t = ? s = 20 km/hr Units, units, units!

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**“A runner’s average speed during the 10 kilometer race was 20 km/hr**

“A runner’s average speed during the 10 kilometer race was 20 km/hr. What was his time?’” Step 3 Set up the formula. FORMULA MUST MATCH UNKNOWN t = d s Formula Plug-in Answer d = 10 km t (hr) = d (km) s (km/hr) t = ? s = 20 km/hr Units, units, units!

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**“A runner’s average speed during the 10 kilometer race was 20 km/hr**

“A runner’s average speed during the 10 kilometer race was 20 km/hr. What was his time?’” Step 4 SUBSTITUTE AND SOLVE Plug-in the numbers and do the math. Check units for answer. Time: 0.5 Hour Formula Plug-in Answer d = 10 km 0.5 hr t = d s 10 km 1 r t = t (hr) 10 km = = 0.5 hr 20 km/hr 20 km/hr s = 20 km/hr Units, units, units!

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**Do the problems 4-5 on your notes.**

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**“You decide to go to Dallas to see friends**

“You decide to go to Dallas to see friends. Your friends tell you that it takes 4 hours to get to Dallas at an average speed of 70 miles per hour. Approximately how many miles is it to their house?” 70 miles per hour Step 1 Read the problem. Draw a picture. Step 2 Write down what you know. GIVEN What are you trying to find? UNKNOWN ? Step 3 Set up the formula. EQUATION Step 4 Plug-in the numbers. SUBSTITUTE Do the math. SOLVE. ANSWER with correct unit. Formula Plug-in Answer d = 280 mi 4 hr t = d = s * t d =70 mi/hr * 4 hr = 280 mi s = 70 mi/hr Units, units, units!

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**Do problem 6 on your notes.**

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**Instantaneous speed (Reading on your speedometer)**

and Average speed (Total distance traveled over total time) Both do not involve direction.

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**What is the difference between speed and velocity?**

55 mi/hr Velocity has speed & direction. 55 mi/hr All of these cars had different velocities because they were traveling in different directions. 55 mi/hr

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**A distance/time graph makes it possible to “see” speed. **

This graph shows how fast the swimmers went during their workout. This graph shows how fast the swimmers went during their workout. Which swimmer swam at a constant (the same) speed throughout her workout? Constant speed Is a straight line Which one stopped during his/her workout? Stopped here 400 meters at 10, 15, & 20 minutes

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Make the speed graph & answer the questions.

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Acceleration

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**Acceleration is defined as the change in velocity over time.**

Any time an object's velocity is changing, we say that the object is accelerating. This brings up an important point. In common language, when things speed up, we say that they are "accelerating," and, when they slow down, we say that they are "decelerating."

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However, in the language of physics, we say that both objects are accelerating, not because both objects are speeding up, but because both objects have changing velocities. POSITIVE ACCELERATION (SPEEDING UP) * NEGATIVE ACCELERATION (DECELERATING) SLOW DOWN

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**Acceleration is defined as the change in velocity over time.**

final velocity – initial velocity time acceleration = Vf - Vi t a =

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**A go-cart started from the top of a hill at 5 meters per second**

A go-cart started from the top of a hill at 5 meters per second. At the bottom of the hill it ended up with a speed of 35 meters per second 6 seconds later. What was the acceleration of the go-cart? Step 1 Read the problem. Draw a picture. 5 m/s top Vf = In 6 s Formula Plug-in Answer Vi= t = a = bottom 35 m/s

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**A go-cart started from the top of a hill at 5 meters per second**

A go-cart started from the top of a hill at 5 meters per second. At the bottom of the hill it ended up with a speed of 35 meters per second 6 seconds later. What was the acceleration of the go-cart? Start: initial Velocity Step 2 Write down what you know. What are you trying to find? 5 m/s top final velocity – initial velocity acceleration = time Vf = 35 m/s 6 s Formula Plug-in Answer Vi= 5 m/s t = 6 s a = ? bottom Finish: final Velocity 35 m/s

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**A go-cart started from the top of a hill at 5 meters per second**

A go-cart started from the top of a hill at 5 meters per second. At the bottom of the hill it ended up with a speed of 35 meters per second 6 seconds later. What was the acceleration of the go-cart? Initial Velocity Step 3 Set up the formula. 5 m/s top Vf - Vi t Vf = 35 m/s Formula Plug-in Answer 6 s Vi= 5 m/s Vf - Vi t t = 6 s a = ? bottom 35 m/s Final Velocity

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**Step 4 Plug-in the numbers. Solve.**

A go-cart started from the top of a hill at 5 meters per second. At the bottom of the hill it ended up with a speed of 35 meters per second 6 seconds later. What was the acceleration of the go-cart? Step 4 Plug-in the numbers. Solve. Vf = 35 m/s Formula Plug-in Answer Vi= 5 m/s Vf - Vi 35m/s – 5 m/s 30 m/s = 5 m/s2 t = 6 s t 6s 6 s a = 5 m/s2

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**5 m/sec2 5 m/sec increase in speed every second. 0 sec 0 m/sec**

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**Do the problems 8-9 on your notes.**

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**70 mi/h 70 mi/h 70 mi/h 70 mi/h 70 mi/h 70 mi/h**

Velocity involves both speed and direction. Changing velocity does not have to necessarily involve a change in speed. It could just involve a change in direction. 70 mi/h 70 mi/h 70 mi/h

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**Think Differently About Acceleration**

1. Consider a car moving at a constant speed of 55 mph while turning in a circle. Constant Speed of 55 mph 2. The car's velocity is not constant, even though the speed is constant. 3. WHY? This is because the direction of motion is constantly changing while the car is turning around the track. 4. Since the direction is changing, even though the speed is not, the velocity is changing (velocity involves both speed and direction).

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**Think Differently About Acceleration**

Constant Speed of 55 mph 5. The car is accelerating because its velocity is changing. 6. As a result, the car is accelerating, even though it is neither speeding up nor slowing down.

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Speed of Sound If you shout at a wall that is 40 meters away how long will it take before you hear the echo of your voice. (The speed of sound = 343 m/sec)

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Speed of Sound If you shout at a wall that is 40 meters away how long will it take before you hear the echo of your voice. (The speed of sound = 343 m/sec) V = D = T = 80 T T T = .23 seconds

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Speed of Sound A lightening bolt flashes in the distance and 5 seconds later you hear the clash of thunder. How far away was the lightening? (Speed of sounds = 343 m/sec)

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Speed of Sound A lightening bolt flashes in the distance and 5 seconds later you hear the clash of thunder. How far away was the lightening? (Speed of sounds = 343 m/sec) V = D = D D = 1715 m T

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Speed of Light Light from the sun is traveling at a speed of 186,000 miles/sec. It takes light 8 minutes to reach the Earth. Calculate the distance from the Earth to the sun.

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Speed of Light Light from the sun is traveling at a speed of 186,000 miles/sec. It takes light 8 minutes to reach the Earth. Calculate the distance from the Earth to the sun. V = D ,000 = D T D = 89,280,000 miles

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