Speed and Velocity

1. Speed and Velocity What is speed, velocity and acceleration? How does speed, velocity and acceleration relate to Forces & Motion?

2. How does MOTION relate to POSITION and TIME? Description of MOTION often includes speed and is a change in position. SPEED then is the rate of change in position or the “rate of motion.” QUESTION: Do you have to see something move to know that motion has taken place? ANSWER: No – because the only thing needed is a reference point to see that something has changed position.

3. Measures of Speed 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. Now, let’s say you are on a highway, a car may travel at the same speed for a long period of time this would be… constant speed. This is the speed that does not vary – cruise control.

5. Katy Houston - - - - - - - - - - - • Now, let’s say that you are trying to determine the distance you are going to traveled in a given amount of time by the time – this would be… average speed. Speed is the distance traveled per unit of time.

6. d s = t distance speed = time Calculating Speed Distance, Speed and Time is shown in the equation: ...or shortened: s = Speed d = Distance t = Time

7. The equation reads - but it can be rearranged to solve for any variable. So, to find DISTANCE, we need to MULTIPLY speed and time. divide d d t = s = d = s x t D t s meters And, to find TIME, we need to DIVIDE distance by the speed. T S m/s seconds multiply Manipulating the Equation

8. 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 Substitute the numbers. Solve. Box Answer with UNITS!

9. 110 miles 2 hours Formula Substitute Answer d = t = s = Units, units, units! Consider the problem… “A car traveled 110 miles in 2 hours.” Step 1 Read the problem. Draw a picture.

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

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

12. 110 miles 2 hours d 110 mi S = 55 mi/hr S = S = t 2 hr 55 mi/hr “A car traveled 110 miles in 2 hours.” Step 4 Substitute the numbers. Solve. Box Answer with Units. Formula Substitute Answer 110 mi d = 2 hours t = s = Units, units, units!

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

14. 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 Substitute Answer d = t = s = Units, units, units!

15. “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 Substitute Answer 10 km d = ? t = 20 km/hr s = Units, units, units!

16. d t = s “A runner’s average speed during the 10 kilometer race was 20 km/hr. What was his time?’” Step 3 Set up the formula. Speed of runner: 20 km/hr 10 km Formula Substitute Answer 10 km d = ? t = 20 km/hr s = Units, units, units!

17. d 10 km t = t = s 20 km/hr “A runner’s average speed during the 10 kilometer race was 20 km/hr. What was his time?’” Step 4 Substitute the numbers. Solve. Box Answer with Units. Formula Substitute Answer 10 km d = 0.5 hr t = 0.5 hr 20 km/hr s = If the runner’s average speed was 20 km/hr during the 10km race, the runner’s time was 0.5 hours. Units, units, units!

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

19. ? Formula Substitute Answer “You decide to go to Dallas to visit your 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 3 Set up the formula. Step 1 Read the problem. Draw a picture. Step 4 Substitute the numbers. Solve. Box Answer with units. Step 2 Write down what you know. What are you trying to find? 280 mi d = 4 hr t = d = s x t d = 280 miles d = 70mi/hr x 4 hr 70 mi/hr s = Units, units, units! If I drive 4 hours at 40mph, the distance from Houston to Dallas is 280 miles.

20. Do problem 6 on your notes.

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 in your notes & answer the questions.

23. VELOCITY. • Instantaneous speed(Reading on your speedometer) and average speeddoes not involve direction. So, what would involve both speed and direction……..

24. Velocityhas speed &direction. • What is the difference between speed and velocity? 55 mi/hr All of these cars had the same SPEED but, different VELOCITIESbecause they were traveling in different directions. 55 mi/hr If you change direction, you have changed your velocity – and if you have changed your speed, you have changed your velocity. Therefore, any change in speed OR direction is a change in velocity! 55 mi/hr

25. Why is it important to know the VELOCITY of a tornado?

26. Acceleration Here we are back at the same questions…… What is speed, velocity and acceleration? How does speed, velocity and acceleration relate to Forces & Motion?

27. (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.

28. Types of Acceleration • Positive Acceleration • Velocity and acceleration are in the same direction. • Object SPEEDS up. • Negative Acceleration • Velocity and acceleration are in opposite • direction. • Object SLOWS down.

29. Formula Substitute Answer Vf = Vi= t = a = 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 In 6 s bottom 35 m/s

30. A go-cart started from the top of a hill at 5 meters persecond. 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: initialVelocity Step 2 Write down what you know. What are you trying to find? 5 m/s top 35 m/s Vf = 6 s Formula Substitute Answer Vi= 5 m/s t = 6 s ? a = bottom Finish: final Velocity 35 m/s

31. 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? Vf - Vi Vf - Vi t t InitialVelocity Step 3 Set up the formula. 5 m/s top 35 m/s Vf = Formula Substitute Answer 6 s Vi= 5 m/s t = 6 s ? a = bottom Final Velocity 35 m/s

32. 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? Formula Answer Substitute Vf - Vi 35m/s– 5 m/s 30 m/s = 6 s t 6s Step 4 Substitute the numbers. Solve. Box Answer with Units. 35 m/s Vf = Vi= 5 m/s 5 m/s2 t = 6 s a = 5 m/s2 The go-cart that traveled from 5m/s to 35 m/s in 6 seconds had an acceleration of 5m/s2.

33. Do the problems 7-9 on your notes.