1. 1 Chapter 2 Motion F. Morales

2. 2 CHAPTER OUTLINE  Motion Motion  Vectors Vectors  History of Motion History of Motion  Speed & Velocity Speed & Velocity  Acceleration Acceleration  Free Fall Free Fall  Projectiles Projectiles

3. 3 MOTION  Motion is described as change in position of an object relative to a frame of reference.  Frame of reference is a coordinate system that is assumed to be stationary.  Kinematics is the scientific description of motion without regard to its cause.

4. 4 MOTION Motion can be described as: UniformCar cruising down a highway Non-uniformSkier sliding down a slope LinearSprinters running along a straight line Non-linearGolf ball flying in a trajectory

5. 5 VECTORS Two types of quantities exist in science: Scalar:expressed using only a magnitude examples: mass, time, length, speed Vector:expressed with a magnitude and direction examples: velocity, acceleration, force

6. 6 VECTORS  Vectors are represented by arrows.  The length represents the magnitude.  The arrowhead represents the direction. 3 miles 4 miles 1 mile East West North

7. 7 VECTORS  What statements can you make about the motion of the cars and the man shown below?

8. 8 ADDITION OF VECTORS When two vectors are parallel and in the same direction, their resultant is their sum. A motor boat travels 10 km/h relative to the water. If the water flow is 5 km/h, what is the boat ’ s speed relative to the the shore, if the boat is heading directly downstream? 15 km/h

9. 9 ADDITION OF VECTORS When two vectors are parallel and opposite in direction, their resultant is their difference. In the previous problem, what is the boat ’ s speed if it is heading upstream? 5 km/h 10 km/h 5 km/h

10. 10 HISTORY OF MOTION  Aristotle believed that motion on earth required forces. He believed that a body would not move unless subjected to a force. Based on this view, the normal state of objects was rest.

11. 11 HISTORY OF MOTION  Galileo believed that time was an important factor in describing motion. He studied change of various quantities with time, and introduced concept of rate to the study of motion.

12. 12 SPEED  Speed is the rate of change of distance with time.  Instantaneous speed is speed at a given time.

13. 13 Example 1: Determine the speed (km/h) of a biker who travels 10 km in 12 minutes. d = 10 km t = 12 min s = ??? s = 50 km/h

14. 14 Example 2: Sound travels at about 340 m/s. 5.0 seconds after seeing the lightning in a cloud, you hear thunder. How far away is the cloud? s = 340 m/s t = 5.0 s d = ??? d = 1700 m

15. 15 Example 3: Mary jogs 1.5 miles from her home to the track in 20 min, and returns home in 25 min. What is Mary ’ s average speed (mi/h) for the entire distance? = 4.0 mi/h

16. 16 Example 4: A racecar travels 180 km in 72 minutes. What is the speed of the racecar in km/h? d = 180 km t = 72 min s = ??? s = 150 km/h

17. 17 VELOCITY  Velocity is speed in a particular direction.  Velocity is a vector quantity.  Velocity is the rate of change of displacement with time.  Instantaneous velocity is velocity at a given time.

18. 18 DISTANCE VS. DISPLACEMENT  Displacement is the shortest distance between two points.  Distance between points H and C can depend on the path taken, but displacement is the same.

19. 19 Example 1: A man walks 3.0 mile north, then turns and walks back to his starting point. If it took him 2.5 hours to complete his walk, determine his average speed and average velocity. 3 mi Distance = 6 mi Displacement = 0 mi

20. 20 Example 1: Calculate avg. speed Calculate avg. velocity

21. 21 Example 2: A jogger runs 200 m around a circular track in 25 seconds. What are his average speed and velocity?

22. 22 ACCELERATION  Acceleration is the rate of change of velocity with time.

23. 23 ACCELERATION  Acceleration occurs whenever there is a change in motion. Speeding up Slowing down Turning

24. 24 ACCELERATION vs. DECELERATION When acceleration and velocity are in the same direction, speed increases.

25. 25 ACCELERATION vs. DECELERATION When acceleration and velocity are in the opposite direction, speed decreases.

26. 26 ACCELERATION vs. DECELERATION When acceleration and velocity are perpendicular to each other, turning occurs.

27. 27 Example 1: Starting from rest, an airliner achieves takeoff velocity of 100 m/s in 50 seconds. What is its acceleration? v 0 = 0 m/s v f = 100 m/s t = 50 s a = ??? a = 2 m/s 2

28. 28 Example 2: A satellite ’ s velocity is 15,000 m/s. After 30 seconds its velocity reaches 30,000 m/s. What is the satellite ’ s acceleration? v 0 = 15000 m/s v f = 30000 m/s t= 30 s a = ??? a = 500 m/s 2

29. 29 Example 3: A car accelerates from rest and reaches a velocity of 25 m/s in 4.8 s. What is the car ’ s acceleration? v 0 = 0 m/s v f = 25 m/s t= 4.8 s a = ??? a = 5.2 m/s 2

30. 30 ACCELERATION  For an accelerating object, velocity increases uniformly with time. v f = v 0 + a t When v 0 = 0 = a t a = 2 m/s 2 t v f 1 s2 m/ s 2 s4 m/ s 3 s6 m/ s v f = (2 m/s 2 )(1 s) v f = (2 m/s 2 )(2 s) v f = (2 m/s 2 )(3 s)

31. 31 ACCELERATION a = 2 m/s 2 t d  For an accelerating object, distance increases non-uniformly with time. 1 s1 m 2 s4 m 3 s9 m

32. 32 Example 1: A rocket is given a constant acceleration of 2.0 m/s 2. What is its velocity 90 seconds after liftoff? v 0 = 0 m/s a = 2.0 m/s 2 t= 90 s v f = ??? v f = a t Since v 0 = 0 = (2.0 m/s 2 )(90 s) v f = 180 m/s

33. 33 Example 2: The driver of a car traveling at a velocity of 30 m/s slams on the brakes and stops in 5 s. v 0 = 30 m/s v f = 0 m/s t = 5 s a = ??? a = - 6 m/s 2 a) What is the car ’ s acceleration? Indicates deceleration

34. 34 Example 2: The driver of a car traveling at a velocity of 30 m/s slams on the brakes and stops in 5 s. a = - 6 m/s 2 t = 5 s d = ??? d = 75 m b) How far does the car travel while braking? = 0.5 (6 m/s 2 )(5 s) 2 Ignore the negative sign

35. 35 Example 3: A car accelerates from rest at a rate of 3.5 m/s 2 for 4.0 seconds. v 0 = 0 m/s a = 3.5 m/s 2 t = 4.0 s v f = ??? v f = 14 m/s a) What is the car ’ s velocity after 4.0 s? v f = a t= (3.5 m/s 2 )(4.0 s)

36. 36 Example 3: A car accelerates from rest at a rate of 3.5 m/s 2 for 4.0 seconds. a = 3.5 m/s 2 t= 4.0 s d = ??? d = 28 m b)What distance does the car travel during this time? = 0.5 (3.5 m/s 2 )(4.0 s) 2

37. 37 FREE FALL  Galileo questioned Aristotle ’ s view that objects fell because of their “ earthiness ”. According to a popular story, he dropped stones of different masses from the tower of Pisa and determined experimentally how mass of objects affected their rate of fall.  Galileo was the first person to correctly understand the motion of bodies falling under the force of gravity (free fall).

38. 38 FREE FALL  In free fall, no force other than gravity acts on the object. (Air resistance is ignored for simplification).  In free fall, all objects fall to the ground at the same rate, regardless of mass. They accelerate at the rate of 9.8 m/s 2 (g).  Velocity and distance of falling objects can be determined by using the following 2 equations: v = g t g = gravity ≈ 10 m/s 2

39. 39 Example 1: A book falls from the balcony of a 12th-floor apartment and smashes to the ground 3.0 s later. g = 10 m/s 2 t = 3.0 s v = ??? v = 30 m/s a)How fast is the book moving just before it hits the ground? v = g t= (10 m/s 2 )(3.0 s)

40. 40 Example 1: g = 10 m/s 2 t = 3.0 s d = ??? d = 45 m b)What distance does the book fall? = 0.5 (10 m/s 2 )(3.0 s) 2 A book falls from the balcony of a 12th-floor apartment and smashes to the ground 3.0 s later.

41. 41 Example 2: g = 10 m/s 2 t = 6.0 s d = ??? d = 180 m = 0.5 (10 m/s 2 )(6.0 s) 2 A rock is dropped in a well and hits the bottom in 6.0 seconds. How deep is the well?

42. 42 FREE FALL In free fall,  velocity increases uniformly with time.  distance increases non- uniformly with time.

43. 43 FREE FALL An object thrown straight upwards,  slows down because of gravity,  stops at the top of its flight,  accelerates downwards to its starting point with a velocity equal and opposite to the original velocity.

44. 44 PROJECTILES  Motion in two dimensions can be analyzed by treating each dimension independently.  Distance traveled horizontally is only dependent on the horizontal velocity.  Height dropped depends only on gravity and can be treated as free fall.

45. 45 Example 1: a) Which rock travels further? A rock thrown from a cliff with a horizontal velocity of 20 m/s reaches the bottom of the cliff in 5 seconds. A second rock is thrown from the same height with a horizontal velocity of 30 m/s. The second rock, since it has a larger horizontal velocity. b) Which rock strikes the ground first? They strike the ground at the same time, since they are both thrown from the same height.

46. 46 THE END