1. ACCELERATION 1

2. Acceleration: is the rate at which the velocity of an object changes relative to time 2

3. ACCELERATION Acceleration: is the rate at which the velocity of an object changes relative to change in time Acceleration = 3

4. ACCELERATION Acceleration: is the rate at which the velocity of an object changes relative to change in time Acceleration = Acceleration is a vector  Because velocity is a vector 4

5. ACCELERATION Velocity has speed and direction  Velocity can be changed by: 1. a change in speed 2. a change in direction 3. a change in both speed and direction  Acceleration can occur with: 1. a change in speed 2. a change in direction 3. a change in both speed and direction 5

6. Acceleration means that the speed of an object is changing, or its direction is, or both.

7. Acceleration Acceleration may result in an object either speeding up or slowing down (or simply changing its direction).

8. Acceleration There is a difference between negative acceleration and deceleration: Negative acceleration is acceleration in the negative direction as defined by the coordinate system. Deceleration occurs when the acceleration is opposite in direction to the velocity.

9. Acceleration If the acceleration is constant, we can find the velocity as a function of time:

10. AVERAGE ACCELERATION Acceleration = = = = 10

11. AVERAGE ACCELERATION EXAMPLE A bicyclist is riding at 15km/hr to the east. In 6.0 seconds he increase his velocity to 45 km/hr to the east. A. What is the average acceleration of the bicyclist? 11

12. AVERAGE ACCELERATION EXAMPLE A bicyclist is riding at 15km/hr to the east. In 6.0 seconds he increase his velocity to 45 km/hr to the east. A. What is the average acceleration of the bicyclist? = = E = (30 km/hr )E = 5.0 km/hr East 6.0 sec 1.0 sec 12

13. AVERAGE ACCELERATION EXAMPLE A bicyclist is riding at 15km/hr to the east. In 6.0 seconds he increase his velocity to 45 km/hr to the east. A. What is the average acceleration of the bicyclist? (5.0 km/hr /sec) E 13

14. AVERAGE ACCELERATION EXAMPLE A bicyclist is riding at 15km/hr to the east. In 6.0 seconds he increase his velocity to 45 km/hr to the east. A. What is the acceleration of the bicyclist? (5.0 km/hr /sec) E the average change in his velocity was 5.0 km/hr E, in each passing second. 14

15. AVERAGE ACCELERATION EXAMPLE A bicyclist is riding at 15km/hr to the east. In 6.0 seconds he increase his velocity to 45 km/hr to the east. A. What is the acceleration of the bicyclist? (5.0 km/hr /sec) E the average change in his velocity was 5.0 km/hr E, in each passing second. The acceleration of the bicyclist was probably not uniform 15

16. AVERAGE ACCELERATION Acceleration can be positive or negative 16

17. AVERAGE ACCELERATION EXAMPLE The same bicyclist is reducing his velocity

18. AVERAGE ACCELERATION EXAMPLE A bicyclist is riding at 45km/hr to the east. In 6.0 seconds he decrease his velocity to 15 km/hr to the east. A. What is the average acceleration of the bicyclist? 18

19. AVERAGE ACCELERATION EXAMPLE A bicyclist is riding at 45km/hr to the east. In 6.0 seconds he decrease his velocity to 15 km/hr to the east. A. What is the average acceleration of the bicyclist? = = E = 19

20. AVERAGE ACCELERATION EXAMPLE A bicyclist is riding at 45km/hr to the east. In 6.0 seconds he decrease his velocity to 15 km/hr to the east. A. What is the acceleration of the bicyclist? (-5.0 km/hr /sec) E the average change in his velocity was -5.0 km/hr E, in each passing second. The acceleration of the bicyclist was probably not uniform 20

21. Instantaneous Acceleration The acceleration of an object for a very short period of time Instantaneous Acceleration (a) a = Δ time is approaching zero a = Δt can never be zero, the equation would be undefined

22. Instantaneous Acceleration The acceleration of an object for a very short period of time Instantaneous Acceleration (a) a = Instantaneous Acceleration is most often used when graphing the motion of an object

23. Acceleration When working with acceleration in our course we will be using CONSTANT ACCELERATION that is our accelerations will not vary

24. Acceleration Problems A train has an initial velocity of 2.1 m/s East. It accelerates for 15 seconds and achieves a velocity of 3.5 m/s East. A. What is the acceleration of this train? B. Convert these velocities into equivalent km/hr.

25. Acceleration Problems A train has an initial velocity of 2.1 m/s East. It accelerates for 15 seconds and achieves a velocity of 3.5 m/s East. A. What is the acceleration of this train? (0.93m/s/s = 0.93m/s 2 B. Convert these velocities into equivalent km/hr.

26. Acceleration Problems A train has an initial velocity of 2.1 m/s East. It accelerates for 15 seconds and achieves a velocity of 3.5 m/s East. A. What is the acceleration of this train? (0.93m/s/s = 0.93m/s 2 B. Convert these velocities into equivalent km/hr. 2.1 m/s 7.6 km/hr 3.5 m/s 13 km/hr

27. Acceleration Due to Gravity Acceleration due to gravity in a FREE FALL A FREE FALL occurs when a mass is falling solely under the force of gravity

28. Figure 2-14 Free fall and air resistance

30. Acceleration Due to Gravity Acceleration due to gravity in a FREE FALL A FREE FALL occurs when a mass is falling solely under the force of gravity

31. Acceleration Due to Gravity Acceleration due to gravity in a FREE FALL A FREE FALL occurs when a mass is falling solely under the force of gravity No air resistance is occurring

32. Acceleration Due to Gravity Acceleration due to gravity in a FREE FALL A FREE FALL occurs when a mass is falling solely under the force of gravity No air resistance is occurring Only gravity is influencing a mass’s change in velocity

33. Acceleration Due to Gravity Acceleration due to gravity in a FREE FALL A FREE FALL occurs when a mass is falling solely under the force of gravity No air resistance is occurring Only gravity is influencing a mass’s change in velocity This does not happen on earth

34. Acceleration Due to Gravity Acceleration due to gravity in a FREE FALL A FREE FALL occurs when a mass is falling solely under the force of gravity No air resistance is occurring Only gravity is influencing a mass’s change in velocity This does not happen on earth, but we pretend that it does for simplicity

35. Acceleration Due to Gravity Free Fall near Earth’s Surface Acceleration of the mass is -9.81 m/s 2 a = g = -9.81 m/s 2

36. Acceleration Due to Gravity Free Fall near Earth’s Surface Acceleration of the mass is -9.81 m/s 2 a = g = -9.81 m/s 2 This acceleration varies slightly by location dependent on radius of earth at particular location density of earth at particular location

37. Acceleration Due to Gravity Free Fall near Earth’s Surface Acceleration of the mass is -9.81 m/s 2 a = g = -9.81 m/s 2 This acceleration varies slightly by location dependent on radius of earth at particular location density of earth at particular location As distance above earth’s surface increases the acceleration due to earth’s gravity decreases

38. Acceleration Due to Gravity Free Fall near Earth’s Surface Acceleration of the mass is -9.81 m/s 2 a = g = -9.81 m/s 2 This acceleration varies slightly by location dependent on radius of earth at particular location density of earth at particular location As distance above earth’s surface increases the acceleration due to earth’s gravity decreases More on this later in the course

39. Acceleration Due to Gravity Earth

40. Acceleration Due to Gravity The gravitational acceleration is about -9.8m/s 2 for a very small distance above the earth’s surface Not to scale Earth

41. Acceleration Due to Gravity The gravitational acceleration is about 9.8m/s 2 for a very small distance above the earth’s surface After about 12 km it becomes≈ 9.79m/s 2 Not to scale Earth

42. Acceleration Due to Gravity The gravitational acceleration is about -9.8m/s 2 for a very small distance above the earth’s surface After about +12 km it becomes≈ -9.79m/s 2 As distance above earth increases this rate of gravitational acceleration decreases. Not to scale Earth

43. Acceleration Due to Gravity The gravitational acceleration is about -9.8m/s 2 for a very small distance above the earth’s surface After about +12 km it becomes≈ -9.79m/s 2 A distance above earth increases this rate of gravitational acceleration decreases. g will never reach zero Not to scale Earth

44. Gravitational Problems A ball is dropped from the top of a tall building. A.What is the original velocity of the ball? A. What is its velocity in m/s after it falls for 5.0 seconds? B.Why isn’t air resistance factored into our answer?

45. Gravitational Problems A ball is dropped vertically from the top of a tall building. A.What is the original vertical velocity of the ball? zero m/s, it was dropped NOT thrown vertically A. What is its velocity in m/s after it falls for 5.0 seconds? B.Why isn’t air resistance factored into our answer?

46. Gravitational Problems A ball is dropped vertically from the top of a tall building. A.What is the original vertical velocity of the ball? zero m/s, it was dropped NOT thrown vertically A. What is its velocity in m/s after it falls for 5.0 seconds? -49 m/s B.Why isn’t air resistance factored into our answer?

47. Gravitational Problems A ball is dropped vertically from the top of a tall building. A.What is the original vertical velocity of the ball? zero m/s, it was dropped NOT thrown vertically A. What is its velocity in m/s after it falls for 5.0 seconds? -49 m/s B.Why isn’t air resistance factored into our answer? We ignore air resistance in this course