1 Speed and Velocity What is speed velocity

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1 Speed and Velocity What is speed, velocity and acceleration? Speed and Velocity (Use

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

2 Speed is the distance traveled per unit of time. Speed (s) = distance

2 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)

3 3 TYPES OF SPEED Instantaneous, Average, Constant Pretend you are looking at your

3 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.

4 B. Constant Speed is when the object covers equal distances in equal amounts

4 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 . . . or shortened: Average Speed is: Total distance = distance traveled all over Total time = final time (end) minus initial time (beginning)

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

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 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

6 Consider the problem… “A car traveled 110 miles in 2 hours. ” Step

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

7 “A car traveled 110 miles in 2 hours. ” Step 2 Write down

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

8 “A car traveled 110 miles in 2 hours. ” Step 3 Set up

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

9 “A car traveled 110 miles in 2 hours. ” Step 3 Formula d

9 “A car traveled 110 miles in 2 hours. ” Step 3 Formula d = 110 miles d t = 2 hours S= s= t Set up the formula. EQUATION Plug-in Units, units! Answer

10 “A car traveled 110 miles in 2 hours. ” Step 4 Plug-in the

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

11 Do the problems 1 -3 on your notes.

11 Do the problems 1 -3 on your notes.

12 Consider the problem… “A runner’s average speed during the 10 kilometer race was

12 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. Speed of runner: 20 km/hr d= t= s= CIRCLE AND LABEL INFO PROVIDED! 10 km Formula Plug-in Units, units! Answer

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

13 “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. What are you trying to find? Speed of runner: 20 km/hr d = 10 km GIVEN UNKNOWN 10 km Formula Plug-in t= s = 20 km/hr Units, units! Answer

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

14 “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 = 10 km Formula t= t (hr) = s = 20 km/hr d s Plug-in d (km) s (km/hr) Units, units! Answer

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

15 “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 d = 10 km t = 0. 5 hr s = 20 km/hr Formula t= d s Plug-in t = 10 km (hr) 20 km/hr Units, units! Answer 10 km =0. 5 20 km/hr hr

16 Do the problems 4 -5 on your notes.

16 Do the problems 4 -5 on your notes.

17 “You decide to go to Dallas to see friends. Your friends tell you

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 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. d = 280 mi Formula t = 4 hr s = 70 mi/hr d=s*t Plug-in Answer d =70 mi/hr * 4 hr = 280 mi Units, units!

18 Do problem 6 on your notes.

18 Do problem 6 on your notes.

19 Instantaneous speed (Reading on your speedometer) and Average speed distance traveled over (Total

19 Instantaneous speed (Reading on your speedometer) and Average speed distance traveled over (Total time) Both do not involve direction.

20 What is the difference between speed and velocity? r i/h m 5 5

20 What is the difference between speed and velocity? r i/h m 5 5 Velocity has speed & direction. 55 mi/hr All of these cars had different velocities because they were traveling in different directions. 55 mi /h r

21 A distance/time graph makes it possible to “see” speed. This graph shows how

21 A distance/time graph makes it possible to “see” speed. This graph shows how fast the swimmers went during their workout. d e e Which swimmer swam at a constant (the same) speed throughout her workout? p s t n a t s n Which one stopped during his/her workout? Co Is a g ai in tl e h r st Stopped here 400 meters at 10, 15, & 20 minutes

22 Make the speed graph & answer the questions.

22 Make the speed graph & answer the questions.

23 Acceleration

23 Acceleration

24 Acceleration is defined as the change in velocity over time. Any time an

24 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. "

25 However, in the language of physics, we say that both objects are accelerating,

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

26 Acceleration is defined as the change in velocity over time. (change) in velocity

26 Acceleration is defined as the change in velocity over time. (change) in velocity acceleration = time final velocity – initial velocity a= time Vf - V i t

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

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. Vf = V i= Formula Plug-in Answer t= a= bottom 35 m/s top In 6 s

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

28 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: Step 2 acceleration = Write down what you know. What are you trying to find? final velocity – initial velocity time Vf = 35 m/s Vi= 5 m/s Formula Plug-in Answer 6 s t= 6 s a= bottom 35 m/s Finish: final Velocity initial Velocity 5 m/s top

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

29 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 3 Initial Velocity Set up the formula. 5 m/s top Vf - V i t Vf = 35 m/s Vi= 5 m/s t= 6 s a= Formula Plug-in Answer 6 s Vf - V i t bottom 35 m/s Final Velocity

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

30 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 Vf = 35 m/s Vi= 5 m/s t= 6 s a = 5 m/s 2 Formula Vf - V i t Plug-in the numbers. Solve. Plug-in 35 m/s – 5 m/s 6 s Answer 30 m/s 6 s = 5 m/s 2

31 5 m/sec 2 • • 5 0 1 2 3 4 5 6

31 5 m/sec 2 • • 5 0 1 2 3 4 5 6 m/sec sec increase in speed every second. 0 m/sec 5 m/sec 10 m/sec 15 m/sec 20 m/sec 25 m/sec 30 m/sec

32 Do the problems 8 -9 on your notes.

32 Do the problems 8 -9 on your notes.

33 i/h m m 70 i/h 70 70 /h i m Velocity involves both

33 i/h m m 70 i/h 70 70 /h i m 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 m i / h i/h 70 m i/h

34 Think Differently About Acceleration 1. Consider a car moving at a constant speed

34 Think Differently About Acceleration 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. Constant Speed of 55 mph 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).

35 Think Differently About Acceleration 5. The car is accelerating because its velocity is

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

36 Speed of Sound • If you shout at a wall that is 40

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 voice. (The speed of sound = 343 m/sec)

37 Speed of Sound • If you shout at a wall that is 40

37 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 343 = 80 343 T = 80 T T 343 T =. 23 seconds

38 Speed of Sound • A lightening bolt flashes in the distance and 5

38 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)

39 Speed of Sound • A lightening bolt flashes in the distance and 5

39 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 343 = D D = 1715 m T 5

40 Speed of Light • Light from the sun is traveling at a speed

40 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.

41 Speed of Light • Light from the sun is traveling at a speed

41 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 186, 000 = D T 480 D = 89, 280, 000 miles