1. Honors Physics CHAPTER TWO One Dimensional Kinematics Teacher: Luiz Izola

2. Chapter Preview 1.Position, Distance, and Displacement 2.Average Speed and Velocity 3.Instantaneous Velocity 4.Acceleration 5.Motion with Constant Acceleration 6.Freely Falling Objects

3. Learning Objectives  How to analyze one-dimensional motion related to displacement, time, speed, and velocity.  How to distinguish between accelerated and non-accelerated motion.

4. Introduction  Mechanics is the study of how objects move, how they respond to external forces, and how other factors, such as size, mass, mass distribution affect their motion.  Kinematics, from Greek kinema, means motion. It is the study of motion and how to describe it, without regard for how the motion was caused.

5. Displacement  Simplest form of motion: One-dimensional  Frame of reference: In order to analyze any motion related problem, we need to have a point of reference in order to create logical assumptions.  Displacement: Length from initial position to final on a straight line. SI unit is meter Δx = x f – x i  Lets us try example 2-1: pages 18.

6. Displacement and Velocity  Displacement can be positive or negative, it depends on the direction of the motion.  Read top of page 18.  Velocity – Displacement divided by the time interval during the displacement occurrence. Average Velocity = Δx / Δt, where: Δx = change in position Δt = change in time

7. Displacement and Velocity  Velocity SI unit is: meters/seconds.  Velocity can be positive or negative, depending on sign of displacement.  Time is always positive.  Average velocity is equals to the constant velocity needed to cover the given displacement in a time interval.

8. Practice Session 1.During a race on level ground, Andra runs with an average velocity of 6.02m/s to the east. What is Andra’s displacement after 137 seconds. 2.You drive 4 mi at 30 mi/h and then another 4 mi at 50 mi/h. Is your average speed for the 8 miles: (a) > 40 mi/h (b) = 40 mi/h (c) < 40 mi/h

9. Practice Session 3.A kingfisher is a a bird that catches fish by plunging into water from a height of several meters. If a kingfisher dives from a height of 7.0m with an average speed of 4.00m/s, how long does it take it to reach the water?

10. Practice Session 4.An athlete sprints 50.0m in 8.00s, then stops, and walks slowly back to the starting line in 40.0s. If the “sprint direction” is taken to be positive, what is (a) the average sprint velocity. (b) the average walking velocity, and (c) the average velocity for the complete round trip?

11. Velocity and Speed  Velocity is not the same as speed: Speed does not take into consideration direction.  Velocity can be interpreted by graphs. See Figs. 2-3, 2-4, page 21.  Slope of line is related to average velocity: V avg = Slope = Δy / Δx, where: Δy = Vertical coordinate change Δx = Horizontal coordinate change

12. Instantaneous Velocity  Instantaneous velocity: It is the velocity at a specific time.  One way to determine the instantaneous velocity is to construct a straight-line tangent to the velocity graph line. The point where the lines touch is the instantaneous velocity at that specific time.  See Fig. 2-8, page 24.

13. Acceleration  Acceleration is the rate of velocity change with respect to time.  Average acceleration is calculated by dividing the total velocity change by the time change. a avg = Δv / Δt  SI acceleration units: meters / seconds 2

14. Practice Session 1.A shuttle bus slows down with an average acceleration of -1.8m/s2. How long does it take the bus to slow from 9.0 m/s to a complete stop? 2.Saab advertises a car that goes from 0 to 60mi/hour in 6.2s. What is the average acceleration of the car? 3.An airplane has an average acceleration of 5.6m/s 2 during takeoff. How long does it take for the plane to reach a speed of 150mi/h?

15. Acceleration  Since acceleration is directly proportional to velocity, it has direction and magnitude.  Velocity positive  Acceleration positive  Velocity negative  Acceleration negative  Velocity constant  Acceleration is zero  Slope and shape of a velocity-time graph describes the object’s motion. See Fig 2-10, page 26.

16. Acceleration  A negative acceleration does not mean that speed is decreasing. It is related to direction.  When velocity and acceleration of an object have the same sign, object’s speed increases. Velocity and acceleration point to same direction.  When they have opposite signs, speed decreases. Velocity and acceleration point to opposite directions.

17. Motion with Constant Acceleration  If a particle moves with constant acceleration, the average acceleration is equal to the instant acceleration.  Displacement depends on acceleration, initial velocity, and time.  Velocity as a function of time. (Acceleration is constant) v f = v i + at

18. Motion with Constant Acceleration  Let us try Page 29: Exercise 2-2.  Average Velocity Equation: v avg = ½ (v f + v i )  Position as a Function of Time Equations: x = x i + ½ (v f + v i )t x = x i + v i t + ½at 2  Let us try Pg. 30: 2-5, Pg. 32: 2-3, 2-6

19. Motion with Constant Acceleration  Velocity as a Function of Position Equation: v f 2 = v i 2 + 2a(x f – x i )  This equation allows as to relate the velocity at one position to the velocity at another position.  Lets us try Pg. 33: 2-7, Pg. 34: 2-8, Pg. 36: 2-9.  Try to learn the Table 2-4, page 34.

20. Displacement with Constant Acceleration  Final velocity depends on initial velocity, acceleration and time. v f = v i + aΔt  Another way to calculate displacement with relation to constant acceleration is: Δx = v i Δt + ½ a(Δt) 2

21. Practice Session 1. A plane starting at rest at one end of a runway undergoes a uniform acceleration of 4.8m/s 2 for 15 seconds before takeoff. What is the speed at takeoff? How long must the runway be for the plane to be able to take off?

22. Final Velocity  Final velocity depends on initial velocity, acceleration, and displacement.  Therefore, we can calculate the final velocity after any displacement as follows: v f 2 = v i 2 + 2a Δx

23. Practice Session 1. A person pushing a stroller from rest, uniformly accelerating at a rate of 0.500 m/s 2. What is the velocity of the stroller after it has traveled 4.75 m?

24. Falling Objects  Free-falling bodies have constant acceleration.  See picture, page 37. What do you think?  If air resistance is disregarded, objects dropped near the surface of the planet fall with the same constant acceleration. This acceleration is due to gravity, and the motion is referred to as Free Fall.

25. Falling Objects  Gravity’s Acceleration: a g = 9.81 m/s 2  Because an object in free fall is acted on only by gravity, a g is also known as free-fall acceleration.  Acceleration is constant during upward and downward motion.  Let us talk about Fig. 2-17, page 38.

26. Practice Session  Jason hits a volleyball so that it moves with an initial velocity of 6.0 m/s straight upward. If the volleyball starts from 2.0 m above the floor. How long it will be in the air before it strikes the floor?  Let us try page 39: 2-10, page 40: 2-11, page 42: 2-12

27. Homework  Page 46: #1, #3  Page 47: #7, #9, #11, #15  Page 48: #27, #29, #31, #33, #39  Page 49: #43, #45, #47  Page 50: #63, #65, #75, #77