2. Motion Speed, acceleration, momentum

3. What is motion? Motion is your change in position from one point to another...

4. Speed Speed is the rate of change of position. Speed is the rate of change of position.

5. Speed Speed = Distance ÷ Time Speed = Distance ÷ Time D_ D_ S T Example: A car travels 300km in 6 hours. What is the speed of the car?

6. Answer: Speed = distance ÷ time Speed = distance ÷ time Speed = 300km ÷ 6 hours Speed = 300km ÷ 6 hours Speed = 50km/hr Speed = 50km/hr

7. More practice 1. How far can a plane travel if it flies 800km/hr for 9 hours? 1. How far can a plane travel if it flies 800km/hr for 9 hours? 2. How long does it take a ship to go 500 km if it travels at a speed of 50km/hr? 2. How long does it take a ship to go 500 km if it travels at a speed of 50km/hr?

8. Answer 1. D S T S TD 800 9 800km ▪ 9hrs = 7200km hr hr

9. Answer 2. D S T S T 500 500 50 T 50 T 500km ÷ 50km = 10 hrs hr hr

10. Velocity Speed in a given direction. Speed in a given direction. What is the velocity of a boat that travels from Sheboygan to Milwaukee (50 miles) in 60 minutes? What is the velocity of a boat that travels from Sheboygan to Milwaukee (50 miles) in 60 minutes?

11. Answer Speed = distance ÷ time Speed = distance ÷ time Speed = 50 miles ÷ 60 minutes Speed = 50 miles ÷ 60 minutes Speed = 0.83 mi/min Speed = 0.83 mi/min Velocity = 0.83 mi/min South Velocity = 0.83 mi/min South

12. Distance-time graphs On your paper, graph the following: On your paper, graph the following: D (m) T (sec) D (m) T (sec) 00 00 57 57 57 57 10 14 10 14 15 21 15 21

14. Was your graph a straight line? A distance-time graph which is a straight line indicates constant speed. A distance-time graph which is a straight line indicates constant speed. In constant speed, the object does not speed up or slow down. In constant speed, the object does not speed up or slow down.

15. Graph the following on a distance- time graph: D (m)T (s) D (m)T (s) 00 00 00 00 51 51 51 51 202 202 453 804 1255

16. 0 1 2 3 4 5

17. Was your graph a curve? A graph that curves on a distance-time graph shows that the object is accelerating A graph that curves on a distance-time graph shows that the object is accelerating

18. Distance-time graphs Describe the motion of the object as shown in the Describe the motion of the object as shown in the graph. graph. From 0-8 sec, constant speed: (25 m/sec); From 8-12 sec, no motion; From 12-16 sec, increase speed; From 16-20 sec, constant speed

19. Speed-time graphs Using the distance-time graph from the last frame, draw a speed time graph. First fill in the table below: Using the distance-time graph from the last frame, draw a speed time graph. First fill in the table below: Average Speed (m/s) Time (sec) ____0 to 8 ____8 to 12 ____12 to 20 25 0 37.5

20. What does your graph look like? Constant speed will be a horizontal line on a speed time graph. Constant speed will be a horizontal line on a speed time graph. If the speed decreases, the line will slant down. If the speed decreases, the line will slant down. If the speed increases, the line will slant up. If the speed increases, the line will slant up.

21. What do the following speed-time graphs depict?

22. Acceleration Change in velocity Change in velocity Can be change in speed or direction Can be change in speed or direction Acceleration = vf-vi/ ∆T Acceleration = vf-vi/ ∆T vf-vi vf-vi at at Vf is final velocity Vi is initial velocity

23. Acceleration problem A roller coaster’s velocity at the top of a hill is 10m/s. Two seconds later it reaches the bottom of the hill with a velocity of 26m/s. What is the acceleration of the roller coaster? A roller coaster’s velocity at the top of a hill is 10m/s. Two seconds later it reaches the bottom of the hill with a velocity of 26m/s. What is the acceleration of the roller coaster?

24. Answer Acceleration = Vf – Vi Acceleration = Vf – Vi / ∆T / ∆T a = 26m/s – 10m/s a = 26m/s – 10m/s 2 s a = 16m/s 2s 2s a = 8m/s/s or 8m/s 2

25. More acceleration problems 1. A car accelerates at a rate of 20mi/hr/s. How long does it take to reach a speed of 80 mi/hr? 2. A car travels at 60 miles per hour around a curve. Is the car accelerating? 3. A car travels in a straight line at 60mi/hr. Is the car accelerating?

26. Answers: 1. Vf – Vi 80mi/hr 80mi/hr a t20mi/hr/s t 4sec = t 2. yes! Because it’s changing direction! 3. no! It’s not changing speed or direction!

27. Deceleration Negative acceleration Negative acceleration Example: A car slows from 60mi/hr to 20mi/hr in 4 seconds. What is its acceleration? Example: A car slows from 60mi/hr to 20mi/hr in 4 seconds. What is its acceleration?

28. Answer: Acceleration = Vf – Vi Acceleration = Vf – Vi / ∆T / ∆T Acceleration = Vf – Vi Acceleration = Vf – Vi t a = 20mi/hr – 60mi/hr a = 20mi/hr – 60mi/hr 4 s a = -40mi/hr 4s 4s a = -10mi/hr/s

29. Review: Distance-time graph of acceleration

30. Distance-time graph of deceleration

31. Review:Speed-time graph of acceleration

32. Review: Speed-time graph of deceleration

33. Review: Distance-time graph of constant speed

34. Momentum Momentum = Mass x Velocity Momentum = Mass x Velocity Which has more momentum: a 140 kg football player moving at 5m/s or a 90 kg quarterback moving at 10m/s? Which has more momentum: a 140 kg football player moving at 5m/s or a 90 kg quarterback moving at 10m/s?

35. Answer: Momentum of the 300lb player is Momentum of the 300lb player is 140 kg x 5 m/s = 700 kg*m/s Momentum of the quarterback is Momentum of the quarterback is 90 kg x 10 m/s = 900 kg*m/s 90 kg x 10 m/s = 900 kg*m/s The quarterback has a greater momentum! The quarterback has a greater momentum!

39. Inelastic collision

41. Elastic collision

42. Two dimensional collision

43. Momentum problems 2 cars are heading east, car A is traveling 30mi/hr, car B is traveling 60mi/hr. Each car has a mass of 900 kg 2 cars are heading east, car A is traveling 30mi/hr, car B is traveling 60mi/hr. Each car has a mass of 900 kg What is the momentum of car A? What is the momentum of car A? What is the momentum of car B? What is the momentum of car B? If car B crashes into car A, what is the total momentum? If car B crashes into car A, what is the total momentum?

44. Answers: P=mv P=mv Car A’s momentum = 30mi/hr x 900 kg Car A’s momentum = 30mi/hr x 900 kg P A = 27000 kg*mi/hr east P A = 27000 kg*mi/hr east Car B’s momentum = 60mi/hr x 900 kg Car B’s momentum = 60mi/hr x 900 kg P B = 54000 kg*mi/hr east Total momentum = P A + P B Total momentum = P A + P B = 27000 + 54000 = 81000 kg*mi/hr east = 27000 + 54000 = 81000 kg*mi/hr east

45. Another momentum problem! Car X is traveling 30mi/hr east, car Y is traveling 60mi/hr west. Each car weighs 900kg. Car X is traveling 30mi/hr east, car Y is traveling 60mi/hr west. Each car weighs 900kg. What is the momentum of car X? What is the momentum of car X? What is the momentum of car Y? What is the momentum of car Y? If car X crashes into car Y, what is the total momentum? If car X crashes into car Y, what is the total momentum?

46. Answers: P=mv P=mv Car X’s momentum = 30mi/hr x 900 kg Car X’s momentum = 30mi/hr x 900 kg P A = 18000kg * mi/hr east P A = 18000kg * mi/hr east Car Y’s momentum = 60mi/hr x 900 kg Car Y’s momentum = 60mi/hr x 900 kg P Y = 54000 kg * mi/hr west Total momentum = P Y - P X Total momentum = P Y - P X = 54000-18000 = 54000-18000 = 36000 kg * mi/hr west = 36000 kg * mi/hr west

47. Which has more momentum?