1. Physics of Motion

2. Frame of Reference- background or object that shows a change in position. Ex. Earth or the Horizon Fixed in place. If an object is moved from here we have had some kind of motion.

3. What is the difference between speed and acceleration? Can a car be speeding very fast and have zero acceleration?

4. Speed Speed is a measure of how much distance is covered in a given amount of time. Speed is a measure of how much distance is covered in a given amount of time. It’s one example of a rate. It’s one example of a rate. Speed is a distance divided by a time Speed is a distance divided by a time S = D/ T S = D/ T

5. UNITS Any distance unit and any time unit can be used to define a speed Any distance unit and any time unit can be used to define a speed Examples km/hr, meters/sec, mi/hr, Examples km/hr, meters/sec, mi/hr, cm/sec, light years/century etc. cm/sec, light years/century etc.

6. Comparing Units 20 km/h 12 mi/h 6 m/s 40 km/h 25 mi/h 11 m/s 60 km/h 37 mi/h 17 m/s 80 km/h 50 mi/h 22 m/s 100 km/h 62 mi/h 28 m/s 120 km/h 75 mi/h 33 m/s 200 km/h ??

7. Comparing Units 20 km/h 12 mi/h 6 m/s 40 km/h 25 mi/h 11 m/s 60 km/h 37 mi/h 17 m/s 80 km/h 50 mi/h 22 m/s 100 km/h 62 mi/h 28 m/s 120 km/h 75 mi/h 33 m/s 200 km/h 120 mi/h ?

8. Comparing Units 20 km/h 12 mi/h 6 m/s 40 km/h 25 mi/h 11 m/s 60 km/h 37 mi/h 17 m/s 80 km/h 50 mi/h 22 m/s 100 km/h 62 mi/h 28 m/s 120 km/h 75 mi/h 33 m/s 200 km/h 120 mi/h 60 m/s

9. Check for Understanding On your team’s whiteboard, write an equation and solve for the average speed when Betty swims 50.0 meters in 27.4 seconds. Be sure to use correct units and state your answer in two or three significant figures. S = D/T = 50.0m/27.4 s = 1.82 m/s

10. Car Trip D = 1.22 m T = 1.13 s 1.37 s Use T = 1.25s S = D/T = 1.22m / 1.25 s = 0.976 m/s = 0.98 m/s = 1.0 m/s

11. Instantaneous vs. Average Speed vs. Constant Speed Instantaneous speed is speed at a particular instant Instantaneous speed is speed at a particular instant Constant speed never changes Constant speed never changes Average speed is total distance covered for a trip divided by total time elapsed Average speed is total distance covered for a trip divided by total time elapsed average speed = total distance/time average speed = total distance/time

12. Check for Understanding What is the difference between instantaneous and average speed? What is the difference between instantaneous and average speed?

13. Examples Find the average speed of a car trip covering 480 km in 6.0 hrs (be sure to write the symbolic equation first) Find the average speed of a car trip covering 480 km in 6.0 hrs (be sure to write the symbolic equation first) S = distance/time = D/T = S = distance/time = D/T = 480 km/ 6.0 h = 80. km/h (note that it’s two significant figures) 480 km/ 6.0 h = 80. km/h (note that it’s two significant figures)

14. What’s Unknown? Start with S = D/T and find an equation for D = and an Equation for T = S x T D/S

15. Memory Trick D = S x T D = S x T S = D/T S = D/T T = D/S T = D/S D ST When solving problems, always write the symbolic equation first

16. Remember your Algebra S = D/T ; multiply both sides by T S = D/T ; multiply both sides by T S x T = D S x T = D D = S x T; divide both sides by S D = S x T; divide both sides by S D/S = T D/S = T T = D/S T = D/S When solving problems, always write the symbolic equation first. Then an equal sign, then put in the known numbers, then solve.

17. Distance Unknown Find the distance covered by a horse running 18 m/s for one minute Find the distance covered by a horse running 18 m/s for one minute D = S x T=18 m/s x 60 sec =1080 m D = S x T=18 m/s x 60 sec =1080 m Try another one; How far can Sarah run if she averages 4.5 m/s for three minutes and 20 seconds? (What are we going to write first?) Try another one; How far can Sarah run if she averages 4.5 m/s for three minutes and 20 seconds? (What are we going to write first?) D = S x T = 4.5 m/s x 3.0 min x 60s/ 1minute = 810 m D = S x T = 4.5 m/s x 3.0 min x 60s/ 1minute = 810 m

18. Question How long does it take a snail creeping at 1.0 cm per second to cross a 2.0 meter walkway? How long does it take a snail creeping at 1.0 cm per second to cross a 2.0 meter walkway? T = D/S T = D/S T = 200 cm/ 1.0 cm/s T = 200 cm/ 1.0 cm/s T = 200 s T = 200 s T = 3 minutes 20 seconds T = 3 minutes 20 seconds

19. Word Problem Practice Write a symbolic equation for this sentence: Write a symbolic equation for this sentence: How long does it take for the Metroliner train to go from NY to Boston, which are 520 km apart, if it averages 127 km/hr? How long does it take for the Metroliner train to go from NY to Boston, which are 520 km apart, if it averages 127 km/hr? Now write in the numbers Now write in the numbers Now find the answer Now find the answer

20. Check for understanding Does a speedometer measure average speed or instantaneous speed? Does a speedometer measure average speed or instantaneous speed? Courtesy of CobraCountry.com

21. Unit Conversion Suppose we want to convert 25 m/s to km/hour Suppose we want to convert 25 m/s to km/hour 25 m/s x 1 km/1000m x 3600s/1 hour = 25 m/s x 1 km/1000m x 3600s/1 hour = This is called the factor-label method This is called the factor-label method 90 km/hr

22. You Try It Convert 125.0 km/hr to meters/sec Convert 125.0 km/hr to meters/sec 125.0 km/hr x 1000m/1 km x 1 hr/3600 sec = 125.0 km/hr x 1000m/1 km x 1 hr/3600 sec = Another word for the “labels” in this method would be the ??? Another word for the “labels” in this method would be the ??? 34.7 m/s

23. Velocity Velocity is speed in a given direction Velocity is speed in a given direction Constant velocity requires both constant speed and constant direction Constant velocity requires both constant speed and constant direction Is a car traveling on a circular track at steady speed moving at constant velocity? Is a car traveling on a circular track at steady speed moving at constant velocity? NO! It’s direction is continually changing. NO! It’s direction is continually changing.

24. Acceleration

25. Acceleration How fast velocity changes How fast velocity changes Acceleration = change of velocity/time Acceleration = change of velocity/time Includes increases and decreases of speed and changes in direction Includes increases and decreases of speed and changes in direction Acceleration (+) Deceleration (-) Acceleration (+) Deceleration (-) a= Vf- Vi/ t a= Vf- Vi/ t Acceleration = a Time = t Acceleration = a Time = t Vf = Final Velocity Vi= Initial Velocity Vf = Final Velocity Vi= Initial Velocity

26. Acceleration Equations a= Vf-Vi/t a= Vf-Vi/t t = Vf-Vi/a t = Vf-Vi/a Vf = (a x t) + Vi Vf = (a x t) + Vi Vi = Vf – (a x t) Vi = Vf – (a x t) UNITS MUST MATCH! UNITS MUST MATCH!

27. Finding Acceleration A car steadily increases its speed each second from 35 to 40 to 45 km/h. What is its acceleration? A car steadily increases its speed each second from 35 to 40 to 45 km/h. What is its acceleration? Answer: 5 km/h/s Answer: 5 km/h/s In 10 seconds a train increases speed from 20 km/h to 40 km/h. What is its acceleration? In 10 seconds a train increases speed from 20 km/h to 40 km/h. What is its acceleration? a = 20km/h ÷ 10s = 2.0 km/h/s a = 20km/h ÷ 10s = 2.0 km/h/s

28. Free Fall In free fall an object’s speed increases by about 10 m/s in each second. In free fall an object’s speed increases by about 10 m/s in each second. v = gt = 9.8t v = gt = 9.8t g = 9.8 m/s/s g = 9.8 m/s/s g = 9.8 m/s 2 g = 9.8 m/s 2 Time to fall(s) Speed (m/s) 00 19.8 219.6 329.4 439.2 549

29. More on Free Fall Due to gravity a = 9.8 m/s 2 = g Due to gravity a = 9.8 m/s 2 = g v = gt v = gt Instantaneous speed = acceleration x time Instantaneous speed = acceleration x time Question: What is the speed of a rock that has fallen from rest for 5.5 seconds? (without air resistance) Question: What is the speed of a rock that has fallen from rest for 5.5 seconds? (without air resistance)

30. Galileo’s Experiment Which would reach the ground first, a marble or a cannonball? Which would reach the ground first, a marble or a cannonball? Courtesy Dan Heller Photography

31. Rising and Falling Rock A rock is thrown upward with 20 m/s. It rises then falls to the height from which thrown. What will be its speed at that height? It’s velocity? A rock is thrown upward with 20 m/s. It rises then falls to the height from which thrown. What will be its speed at that height? It’s velocity? Answer 20 m/s (down) Answer 20 m/s (down) Gravity takes speed away on the way up at 9.8 m/s/s and then gives it back on the way down, at the same rate

32. Distance Fallen What is average speed of an object that falls for 1 second? What is average speed of an object that falls for 1 second? What is distance fallen in this time? What is distance fallen in this time? What is average speed during second second of fall? What is average speed during second second of fall? What is distance fallen in second second? What is distance fallen in second second? What is distance fallen in first two seconds? What is distance fallen in first two seconds? 5 m/s, average of 0 and 10 5m = 5 m/s x 1s 15 m/s, average of 10 and 20 15m = 15m/s x 1s 20m = 5m + 15m

33. The Pattern Distance fallen in t seconds Distance fallen in t seconds d = 1/2gt 2 d = 1/2gt 2 Now if the object is in motion, then you have to account for that as well. Now if the object is in motion, then you have to account for that as well. d= v i t + 1/2gt 2 d= v i t + 1/2gt 2 timedistance 15 220 345 480 5125

34. Falling Apple An apple drops from the tree and hits the ground in two seconds An apple drops from the tree and hits the ground in two seconds What is its speed when it hits? What is its speed when it hits? What is its average speed? What is its average speed? How high did it fall from? How high did it fall from?

35. Free Fall Problem A person is standing on top of a roof, holding two objects. The person drops item A and at the same time throws item b straight up over the edge of the building with an initial speed of 25 m/s. If the building itself is 450 m high, how long will it take both objects to hit the ground and at what speed will they hit the ground with? A person is standing on top of a roof, holding two objects. The person drops item A and at the same time throws item b straight up over the edge of the building with an initial speed of 25 m/s. If the building itself is 450 m high, how long will it take both objects to hit the ground and at what speed will they hit the ground with?

36. Helicopter Problems 1. A Helicopter is rising 5.0 m/s and someone drops a bag from it. After two seconds, what is the bags velocity, how far has the bag fallen and how far below the helicopter is the bag? 1. A Helicopter is rising 5.0 m/s and someone drops a bag from it. After two seconds, what is the bags velocity, how far has the bag fallen and how far below the helicopter is the bag? 2. The helicopter in problem one now descends 5.0 m/s. After two seconds, what is the bags velocity, how far has the bag fallen and how far below the helicopter is the bag? 2. The helicopter in problem one now descends 5.0 m/s. After two seconds, what is the bags velocity, how far has the bag fallen and how far below the helicopter is the bag?

37. Weather Balloon Problem A weather balloon is floating upward at 2.5 m/s above the Earth when it releases a pack of instruments. A weather balloon is floating upward at 2.5 m/s above the Earth when it releases a pack of instruments. A. If the pack hits the ground with a velocity of 73.5 m/s how far did the pack fall? A. If the pack hits the ground with a velocity of 73.5 m/s how far did the pack fall? B. How long did it take for the pack to fall? B. How long did it take for the pack to fall?

38. Air Resistance Why, on earth, does a coin reach the ground faster than a feather? Why, on earth, does a coin reach the ground faster than a feather? What would happen on the moon? What would happen on the moon?

39. Confused? Explain the difference between velocity and acceleration and velocity? Explain the difference between velocity and acceleration and velocity? Is acceleration an example of a velocity? Is acceleration an example of a velocity? Can an object with zero velocity be accelerating? Can an object with zero velocity be accelerating? At the top of its path, the velocity of a rock thrown upward is ________? At the top of its path, the velocity of a rock thrown upward is ________? At the top, its acceleration is _______? At the top, its acceleration is _______?