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  • Slide 1
  • Slide 2
  • 1 Speed and Velocity What is speed, velocity and acceleration? Speed and Velocity (Use with Speed, Velocity and Acceleration handout)
  • Slide 3
  • 2 Speed (s) = distance (d) time (t) Speed is the distance traveled per unit of time. 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)
  • Slide 4
  • 3 Pretend you are looking at your car's speedometer while you are driving. The reading you get from your speedometer is This is the speed that you are traveling at that moment. A. instantaneous speed 3 TYPES OF SPEED Instantaneous, Average, Constant
  • Slide 5
  • 4 C. Average speed is the total distance traveled divided by the total time. It can be calculated using the following formula: speed = distance time...or shortened: Average Speed is: Total distance = all distance traveled over Total time = final time (end) minus initial time (beginning ) B. Constant Speed is when the object covers equal distances in equal amounts of time.
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  • 5 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 4 PLUG IN THE NUMBERS. SUBSTITUTE DO THE MATH SOLVE. Check ANSWER with UNITS Step 3 WRITE FORMULA EQUATION Set up the formula. (The formula should match the unknown.)
  • Slide 7
  • 6 A car traveled 110 miles in 2 hours. Consider the problem d = t = s = FormulaPlug-inAnswer Units, units, units! Step 1Read the problem. Draw a picture. 110 miles 2 hours
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  • 7 A car traveled 110 miles in 2 hours. d = t = s = FormulaPlug-inAnswer Units, units, units! 110 miles 2 hours Step 2Write down what you know. GIVEN What are you trying to find? UNKNOWN 110 miles 2 hours
  • Slide 9
  • 8 A car traveled 110 miles in 2 hours. d = t = s = FormulaPlug-inAnswer Units, units, units! 110 miles 2 hours Step 3Set up the formula. FORMULA SHOULD MATCH THE UNKNOWN s = d t
  • Slide 10
  • 9 A car traveled 110 miles in 2 hours. d = t = s = FormulaPlug-inAnswer Units, units, units! 110 miles 2 hours Step 3Set up the formula. EQUATION d t S =
  • Slide 11
  • 10 A car traveled 110 miles in 2 hours. d = t = s = FormulaPlug-inAnswer Units, units, units! 110 mi 2 hours Step 4Plug-in the numbers. SUBSTITUTE AND SOLVE. CHECK UNITS d t 110 mi 2 hr 55mi/hr 55mi/hr 55mi/hr S =
  • Slide 12
  • 11 Do the problems 1-3 on your notes.
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  • 12 A runners average speed during the 10 kilometer race was 20 km/hr. What was his time? Consider the problem d = t = s = FormulaPlug-inAnswer Units, units, units! Step 1Read the problem. Draw a picture. 10 km Speed of runner: 20 km/hr CIRCLE AND LABEL INFO PROVIDED!
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  • 13 d = t = s = FormulaPlug-inAnswer Units, units, units! 10 km 20 km/hr Step 2 Write down what you know. GIVEN What are you trying to find? UNKNOWN 10 km Speed of runner: 20 km/hr A runners average speed during the 10 kilometer race was 20 km/hr. What was his time?
  • Slide 15
  • 14 FormulaPlug-inAnswer Units, units, units! Step 3Set up the formula. FORMULA MUST MATCH UNKNOWN A runners average speed during the 10 kilometer race was 20 km/hr. What was his time? d = t = s = 10 km 20 km/hr t = d s t (hr) = d (km) s (km/hr )
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  • 15 FormulaPlug-inAnswer Units, units, units! Step 4SUBSTITUTE AND SOLVE Plug-in the numbers and do the math. Check units for answer. 10 km 20 km/hr d = t = s = 10 km 20 km/hr 0.5 hr A runners average speed during the 10 kilometer race was 20 km/hr. What was his time? Time: 0.5 Hour t = d s t (hr) = = 1 r 0.5 hr 10 km 20 km/hr
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  • 16 Do the problems 4-5 on your notes.
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  • 17 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? Step 1 Read the problem. Draw a picture. Step 2Write down what you know. GIVEN What are you trying to find? UNKNOWN Step 4Plug-in the numbers. SUBSTITUTE Do the math. SOLVE. ANSWER with correct unit. Step 3Set up the formula. EQUATION FormulaPlug-inAnswer Units, units, units! d = t = s = 280 mi 70 mi/hr 4 hr ? 70 miles per hour d = s * t = 280 mi d =70 mi/hr * 4 hr
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  • 18 Do problem 6 on your notes.
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  • 19 Instantaneous speed (Reading on your speedometer) and Average speed (Total distance traveled over total time) Both do not involve direction.
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  • 20 What is the difference between speed and velocity? 55 mi/hr All of these cars had different velocities because they were traveling in different directions. Velocity has speed & direction.
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  • 21A distance/time graph makes it possible to see speed. This graph shows how fast the swimmers went during their workout. Which swimmer swam at a constant (the same) speed throughout her workout? Which one stopped during his/her workout? Constant speed Stopped here 400 meters at 10, 15, & 20 minutes Is a straight line A distance/time graph makes it possible to see speed. This graph shows how fast the swimmers went during their workout.
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  • 22 Make the speed graph & answer the questions.
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  • 23 Acceleration
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  • 24 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." Any time an object's velocity is changing, we say that the object is accelerating. Acceleration is defined as the change in velocity over time.
  • Slide 26
  • 25 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
  • Slide 27
  • 26 Acceleration is defined as the change in velocity over time. (change) in velocity time acceleration = final velocity initial velocity time acceleration = V f - V i t a =
  • Slide 28
  • 27 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. top bottom 35 m/s 5 m/s In 6 s V f = Vi=Vi= t = a = FormulaPlug-inAnswer
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  • 28 top bottom 35 m/s 5 m/s 6 s V f = Vi=Vi= t = a = FormulaPlug-inAnswer Step 2Write down what you know. What are you trying to find? 35 m/s 5 m/s 6 s Finish: final Velocity Start: initial Velocity final velocity initial velocity time acceleration = 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?
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  • 29 top bottom 35 m/s 5 m/s 6 s V f = Vi=Vi= t = a = 35 m/s 5 m/s 6 s Final Velocity Initial Velocity Step 3Set up the formula. FormulaPlug-in V f - V i t Answer V f - V i t 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?
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  • 30 V f = Vi=Vi= t = a = FormulaPlug-inAnswer 35 m/s 5 m/s 6 s V f - V i t 35m/s 5 m/s 6s 30 m/s 6 s = 5 m/s 2 Step 4Plug-in the numbers. Solve. 5 m/s 2 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?
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  • 31 5 m/sec 2 5 m/sec increase in speed every second. 0 sec 0 m/sec 1 sec5 m/sec 2 sec 10 m/sec 3 sec 15 m/sec 4 sec20 m/sec 5 sec 25 m/sec 6 sec30 m/sec
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  • 32 Do the problems 8-9 on your notes.
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  • 33 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
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  • 34 Constant Speed of 55 mph 1. Consider a car moving at a constant speed of 55 mph while turning in a circle. 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). Think Differently About Acceleration
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  • 35 Constant Speed of 55 mph 6. As a result, the car is accelerating, even though it is neither speeding up nor slowing down. 5. The car is accelerating because its velocity is changing. Think Differently About Acceleration
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  • 36 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 voic