PHYSICS MR BALDWIN Speed & Velocity 9/15/2014

1. PHYSICS MR BALDWINSpeed & Velocity 9/15/2014 AIM: What is motion and how does it change? DO NOW: What do you understand about the terms speed and acceleration? Home Work:

2. Laws of Motion • Everything in the universe is in nonstop motion. • Motion is the rule, not the exception. • The laws which govern the motion of atoms and stars apply to the motion in our everyday lives.

3. Distance and Displacement Distinction between distance and displacement. Distance traveled (dashed line) is a measure of length along the actual path. Displacement (blue line) is how far the object is from its starting point, regardless of how it got there.

4. Speed & Velocity Speed: time rate of change of distance : how far an object travels in a given time interval Velocity includes directional information: time rate of change of displacement

5. Average Speed & Instantaneous Speed • The instantaneous speed is the speed as given on your speedometer. The speed at that instant. • Speed given by the speedometer • The average speed is the total distance traveled by an object divided by the total time taken to travel that distance. CHECK: Determine the units Unit: m/s; km/h; mph

6. CHECK: Can you write other forms of the equation to determine the other two quantities t & d?

7. Problem Solving Technique: G.U.S.S. • Givens; Unknown; Substitute & Solve • Write out your Givens. • Identify your Unknown.Check for unit consistency. If not…convert! • Substitute into equation (with units) Find an equation relating quantities. • Solve for unknown.

8. QUIZ CHECK.What is the average speed of a car (in km/h & m/s) that travels 240 miles in 6 hours. Given that 1-mile = 1.609 km = 1609 m

9. PHYSICS MR BALDWINSpeed & Velocity 9/17/2014 AIM: What is the difference between constant and changing motion?(What is acceleration?) DO NOW: Look at the runner below. What can you infer about the runner?

10. Look at the picture below. What can you infer about the runner in red shorts?

11. CHECK: Can you write other forms of the equation to determine the other two quantities t & d?

12. QUANTITY & SYMBOL • Distance d • Time t • Velocity; speed v • Mass m UNITS • meters (m; km; mi) • seconds (s) • meters/sec (m/s) • Km/h • mph • kilogram (kg)

13. Uniform & Accelerated Motion • Uniform motion refers to motion that has a constant velocity • Speed & direction remains the same • Such as your car on cruise control • Moving at 50 mph on a straight road • Accelerated motion refers to motion with changing velocity • As you round a curb • Hit the gas or brake

14. Acceleration Acceleration is the change of velocity divided by time. Where a: acceleration; vf: final velocity; vi:initial velocity Determine its Unit. Unit: m/s2

15. What is the acceleration of a car whose speed increases from 15 m/s (about 34 mi/h) to 25 m/s (about 56 mi/h) in 20s?

16. PHYSICS MR BALDWINSpeed & Velocity 9/18/2014 AIM: What is motion and how does it change? DO NOW: A skater increases his speed from 2.0 m/s to 10.0 m/s in 3.0 s. What is his acceleration? Home Work: Worksheet 2.2

17. Check Which of the following statements correctly define acceleration? • Acceleration is the rate of change of displacement of an object. • Acceleration is the rate of change of velocity of an object. • Acceleration is the amount of distance covered in unit time. • Acceleration is the rate of change of speed of an object.

18. Accelerated Motion Acceleration is also a vector. Therefore, we need the sign. Determine the car’s acceleration. What can you infer about the value of the acceleration? Decelerationoccurs when the acceleration is opposite in direction to the velocity.

19. Check What happens when the velocity vector and the acceleration vector of an object in motion are in same direction? • The acceleration of the object increases. • The speed of the object increases. • The object comes to rest. • The speed of the object decreases.

20. Check A car is moving with an initial velocity of vi m/s. After reaching a highway, it moves with a constant acceleration of a m/s2, what will be the velocity (vf) of the car after traveling for t seconds? • vf = vi + at • vf = vi + 2at • vf2 = vi2 + 2at • vf = vi – at • vf = vi + at • vf = vi + 2at • vf2 = vi2 + 2at • vf = vi – at

21. PHYSICS MR BALDWINAccelerated Motion 9/19/2014 AIM: How are acceleration, velocity, distance and time related? DO NOW: Look at the runner in the red shorts below. What can you infer about the runner’s velocity and distance for each time interval?

22. Changing Velocity Acceleration There are two major indicators of the change in velocity in this motion diagram. Can you identify them? The change in the spacing of the dots and the differences in the lengths of the velocity vectors indicate the changes in velocity.

23. Acceleration Changing Velocity Can you identify which one is speeding up and which one is slowing down? If an object speeds up, each subsequent velocity vector is longer. Also, the subsequent distances increases. If the object slows down, … (you fill in the rest)

24. Acceleration Velocity-Time Graphs What can be said about the distances here?

25. Acceleration Velocity-Time Graphs

26. MATHEMATICAL ANALYSIS OF MOTION

27. Relating Acceleration, Speed & Time The acceleration, assumed constant, is the rate of change of velocity.

28. Relating Acceleration, Speed & Time

29. Average Speed & Distance Traveled During Constant Acceleration In addition, as the velocity is increasing at a constant rate, we know that

30. Equations of Motion (Please write on Index cards)

31. SOME KEY PHRASES • OBJECT STARTS FROM REST • OBJECT RELEASED FROM REST • OBJECT DROPPED • OBJECT STOPS • OBJECT COMES TO REST • OBJECT SLOWS TO A HALT INITIAL VELOCITY IS ZERO FINAL VELOCITY IS ZERO

32. MOTION OF FALLING BODIES

33. PHYSICS MR BALDWINFreefall 9/22/2014 AIM: How do we describe the motion of an object in freefall? DO NOW: In your own words, how would you define or describe freefall? Home Work: Freefall worksheet

34. Freefall Motion Near the surface of the Earth, all objects experience approximately the same acceleration due to gravity. Look at the image to the left. What can you infer about the apple’s motion?

35. Uniformly Accelerated Motion Galileo’s Law of Freely Falling Bodies: In the absence of air resistance, all objects, regardless of size, shape or mass, fall with the same acceleration.

36. Uniformly Accelerated Motion The acceleration due to gravity at the Earth’s surface is approximately 9.80 m/s2.

37. CHECK • What is freefall?

38. Equations of Motion

39. Rearrange the formulas letting a = – g

40. NOTE • The equations can be used to find time of flight from speed or distance, respectively. • Remember that an object thrown into the air represents two mirror-image flights, one up and the other down. • Acceleration of an object moving up is negative. • Magnitude of the acceleration up or down is the same

41. PHYSICS MR BALDWINFreefall Motion 9/23/2014 AIM: How is the motion of an object affected when projected upwards? DO NOW: Describe the velocity of an object after it has been thrown vertically upwards with a speed of 20 m/s and returns back to it initial position. Home Work: Worksheet - Acceleration due to gravity

42. Back to “HOW FAR?” • Recall that • But for the object thrown upwards with some velocity, let d become ‘h’ (to stand for height), and vi is different from 0, with the acceleration a = -g (only due to gravity): • DERIVE THE EQUATION FOR HEIGHT

43. Now to “HOW FAST?” • Recall that • But for the object thrown upwards with some vi different from 0, with the acceleration a= -g (only due to gravity): • DERIVE THE EQUATION FOR OBJECT’S VELOCITY.

44. From this, we can answer “HOW LONG” • If we know the height to which the object rises, we can determine HOW LONG it takes to get there. • What happens to the velocity at the top of the object’s motion? • vf = 0 • DERIVE THE EQUATION FOR THE TIME TAKEN FOR THE OBJECT TO REACH MAXIMUM HEIGHT.

45. “HOW LONG”: What goes up must come down • When we throw an object UP and it returns to its initial position, the total displacement is…_________ • Time of FLIGHT is duration of time object is in the air • d = 0 • DERIVE THE EQUATION FOR THE TIME OF FLIGHT

46. TEST YOURSELF:A ball goes up • We have a situation to consider…The ball’s direction of travel is in the OPPOSITE direction of its acceleration. • THUS… • SO, what will happen to the speed as the ball rises? • DECREASE • Let’s say we gave the ball an initial upward velocity of about 40 m/s. • After 2 s, what will the velocity of the ball be? • How long will the ball be in the air? • How far will it rise in the air?

47. http://phet.colorado.edu/sims/projectile-motion/projectile-motion_en.htmlhttp://phet.colorado.edu/sims/projectile-motion/projectile-motion_en.html http://jersey.uoregon.edu/vlab/block/Block.html

48. GRAPHICAL ANALYSIS OF LINEAR MOTION

49. PHYSICS MR BALDWINGraphing Motion 9/29 & 30/2014 AIM: How do we graphically represent the motion of an object? DO NOW: Draw a distance-time graph of the function Draw a velocity-time graph of the function You can USE your calculator. Home Work: Worksheet - Analyzing Graphs of Motion Without Numbers

50. CHECK • Looking at the equation of motion for distance of accelerated motion, what will the resulting distance-time graph look like? • PARABOLA • Looking at the equation of motion for velocity of accelerated motion, what will the resulting velocity-time graph look like? • STRAIGHT LINE (LINEAR)