Speed and Velocity

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

2. distance speed = time Speed is the distance traveled per unit of time.

3. Pretend you are looking at your car's speedometer while you are driving. The reading you get from your speedometer is instantaneous speed… This is the speed that you are traveling at that moment.

4. d s = t distance speed = time • Average speed is the distance traveled divided by the time. Itcan be calculated using the following formula: ...or shortened:

5. Four Step Approach to Solving Problems Step 1 Read the problem. Draw a picture. Step 2 Write down what you know. What are you trying to find? Step 3 Set up the formula. Step 4 Plug-in the numbers. Solve.

6. 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!

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

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

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

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

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

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 10 km Formula Plug-in Answer d = t = s = Units, units, units!

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 10 km Formula Plug-in Answer 10 km d = ? t = 20 km/hr s = Units, units, units!

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

15. d S = t “A runner’s average speed during the 10 kilometer race was 20 km/hr. What was his time?’” Step 4 Plug-in the numbers. Solve. Time: 0.5 Hour Formula Plug-in Answer 10 km d = 20 km 10 km .5 hr 10 km t = = .5 hr = 20 km x t (hr) t (hr) 1 Hr (t) 20 km/hr s = Proportion Problem… Cross multiply and divide… Units, units, units!

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

17. d (mi) 4 hr 70 mi 1 hr “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?” 4 hours 70 miles per hour Step 1 Read the problem. Draw a picture. Step 2 Write down what you know. What are you trying to find? ? Step 3 Set up the formula. Step 4 Plug-in the numbers. Solve. Formula Plug-in Answer 280 mi d = 4 hr s = d / t t = 70mi x 4hr = = 280 mi d x 1hr 70 mi/hr s = 70 mi/hr = d/4 hr Units, units, units!

18. Do problem 6 on your notes.

19. Instantaneous speed(Reading on your speedometer) and average speeddo not involve direction.

20. What is the difference between speed and velocity? 55 mi/hr Velocity has speed &direction. 55 mi/hr All of these cars had different velocitiesbecause they were traveling in different directions. 55 mi/hr

21. A 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? Constant speed Is a straight line Which one stopped during his/her workout? Stopped here 400 meters at 10, 15, & 20 minutes

22. Make the speed graph & answer the questions.

23. Acceleration

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

25. Formula Plug-in Answer 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 Vi= t = a = bottom 35 m/s

26. 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 second6 seconds later. What was the acceleration of the go-cart? Formula Plug-in Answer Start: initialVelocity Step 2 Write down what you know. What are you trying to find? 5 m/s top final velocity – initial velocity acceleration = time 35 m/s Vf = 6 s Vi= 5 m/s t = 6 s ? a = bottom Finish: final Velocity 35 m/s

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 second6 seconds later. What was the acceleration of the go-cart? Vf - Vi Vf - Vi t t InitialVelocity Step 3 Set up the formula. 5 m/s top 35 m/s Vf = Formula Plug-in Answer 6 s Vi= 5 m/s t = 6 s ? a = bottom Final Velocity 35 m/s

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 second6 seconds later. What was the acceleration of the go-cart? Step 4 Plug-in the numbers. Solve. 35 m/s Vf = Formula Plug-in Answer Vi= Vf - Vi 35m/s– 5 m/s 5 m/s 30 m/s = 5 m/s2 6 s t = t 6 s 6s a = 5 m/s2

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

30. 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."

31. 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.

32. 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

33. Constant Speed of 55 mph 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. 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 bothspeed and direction).

34. 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.