1. Physics Chapter 2 Motion in One-Dimension 2.1 Displacement and Velocity 1. Is the book on my desk in motion? Explain your answer. 1. Describe the motion of the vehicles you saw on the way to school. To simplify the concept of motion, we will first consider motion that takes place in one direction.

2. 2.1 Objectives  Describe motion in terms of frame of reference, displacement, time, and velocity.  Calculate the displacement of an object traveling at a known velocity for a specific time interval.  Construct and interpret graphs of position versus time.

3. To measure motion, you must choose a frame of reference. A frame of reference is a system for specifying the precise location of objects in space and time.  Motion  a change in position  Frame of reference  A point against which position is measured  Example: A train traveling between stations  It is in motion when measured against the track.  It is stationary when measured against a seat.  Visual Concepts: Motion and Frame of Reference

4.  x = x f – x i displacement = final position – initial position Straight line distance from the initial position to the final position (change in position) Can be positive or negative Displacement is not always equal to the distance traveled. The SI unit of displacement is the meter, m. Visual Concept: displacement Displacement (  x) 

5. Displacement  What is the displacement for the objects shown? Answer: +70 mm Answer: -60 mm

6. Displacement Sign Conventions  Right (or east) ---> +  Left (or west) ---> –  Up (or north) ----> +  Down (or south) ---> –  These same sign conventions will apply to velocity, acceleration, force, momentum and so on.

7. Average Velocity  The units can be determined from the equation.  SI Units: m/s  Other Possible Units: mi/h, km/h, cm/year  Visual Concept: Average Velocity Average velocity is displacement divided by the time interval.

8. Speed  Speed does not include direction while velocity does.  Velocity describes motion with both a direction and a numerical value (a magnitude).  Speed has no direction, only magnitude.  Speed uses distance rather than displacement  In a round trip, the average velocity is zero but the average speed is not zero.

9. Graphing Motion  How would you describe the motion shown by this graph?  Answer: Constant speed (straight line)  What is the slope of this line?  Answer: 1 m/s  What is the average velocity?  Answer: 1 m/s

10. Graphing Motion  Describe the motion of each object.  Answers  Object 1: constant velocity to the right or upward  Object 2: constant velocity of zero (at rest)  Object 3: constant velocity to the left or downward

11. Instantaneous Velocity  Velocity at a single instant of time  Speedometers in cars measure instantaneous speed.  Determined by finding the slope at a single point (the slope of the tangent)  Necessary when the velocity is not constant What is the slope of the tangent line at t = 3.0 s? –Answer: approximately 12 m/s What is the instantaneous velocity at t = 3.0 s? –Answer: approximately 12 m/s

12. Now what do you think?  Is the book on my desk in motion?  What are some common terms used to describe the motion of objects?

13. Which of the following cars is accelerating? A car shortly after a stoplight turns green A car approaching a red light A car with the cruise control set at 80 km/h A car turning a curve at a constant speed Based on your answers, what is your definition of acceleration? Physics Chapter 2 Motion in One-Dimension 2.2 Acceleration

14. Objectives  Describe motion in terms of changing velocity.  Compare graphical representations of accelerated and nonaccelerated motions.  Apply kinematic equations to calculate distance, time, or velocity under conditions of constant acceleration.

15. Acceleration  The rate at which velocity changes over time  SI Units: (m/s)/s or m/s 2  Other Units: (km/h)/s or (mi/h)/s  An object accelerates if its speed, direction, or both change.  Acceleration = 0 implies a constant velocity (or rest)

16. Practice Problem  Find the acceleration of an amusement park ride that falls from rest to a velocity of 28 m/s downward in 3.0 s.

18. Changes in Velocity, continued  Consider a train moving to the right, so that the displacement and the velocity are positive.  The slope of the velocity-time graph is the average acceleration. –When the velocity in the positive direction is increasing, the acceleration is positive, as at A. –When the velocity is constant, there is no acceleration, as at B. –When the velocity in the positive direction is decreasing, the acceleration is negative, as at C. Visual Concept: Graphical Representations

19. Graphing Velocity  The slope (rise/run) of a velocity/time graph is the acceleration.  Rise is change in v  Run is change in t  This graph shows a constant acceleration.  Average speed is the midpoint.

20. Graph of v vs. t for a train  Describe the motion at points A, B, and C.  A: accelerating (increasing velocity/slope) to the right  B: constant velocity to the right  C: negative acceleration (decreasing velocity/slope) and still moving to the right

21. Motion with Constant Acceleration  When velocity changes by the same amount during each time interval, acceleration is constant.  The relationships between displacement, time, velocity, and constant acceleration are expressed by the equations shown on the next slide. These equations apply to any object moving with constant acceleration.  These equations use the following symbols:  x = displacement v i = initial velocity v f = final velocity  t = time interval

22. Useful Equations 1. 2. 3. 4. 5.

24. Sample Problem Final Velocity After Any Displacement A person pushing a stroller starts 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?

25. Sample Problem, continued 1. Define Given: v i = 0 m/s a = 0.500 m/s 2  x = 4.75 m Unknown: v f = ? Diagram: Choose a coordinate system. The most convenient one has an origin at the initial location of the stroller, as shown above. The positive direction is to the right.

26. Sample Problem, continued 2. Plan Choose an equation or situation: Because the initial velocity, acceleration, and displacement are known, the final velocity can be found using the following equation: Rearrange the equation to isolate the unknown: Take the square root of both sides to isolate v f.

27. Chapter 2 Sample Problem, continued Tip: Think about the physical situation to determine whether to keep the positive or negative answer from the square root. In this case, the stroller starts from rest and ends with a speed of 2.18 m/s. An object that is speeding up and has a positive acceleration must have a positive velocity. So, the final velocity must be positive. 3. Calculate Substitute the values into the equation and solve: 4. Evaluate The stroller’s velocity after accelerating for 4.75 m is 2.18 m/s to the right.

28. Classroom Practice Problems  A bicyclist accelerates from 5.0 m/s to 16 m/s in 8.0 s. Assuming uniform acceleration, what distance does the bicyclist travel during this time interval?

29. Classroom Practice Problems  An aircraft has a landing speed of 83.9 m/s. The landing area of an aircraft carrier is 195 m long. What is the minimum uniform acceleration required for safe landing?

30. Now what do you think?  Which of the following cars is accelerating?  A car shortly after a stoplight turns green  A car approaching a red light  A car with the cruise control set at 80 km/h  A car turning a curve at a constant speed Based on your answers, what is the definition of acceleration? How is acceleration calculated? What are the SI units for acceleration?

31. Physics Chapter 2 Motion in One-Dimension 2.3 Falling Objects Video of hammer and feather experiment on moon http://teachertube.com/vie wVideo.php?video_id=41342

32. Objectives  Relate the motion of a freely falling body to motion with constant acceleration.  Calculate displacement, velocity, and time at various points in the motion of a freely falling object.  Compare the motions of different objects in free fall.

33. Free Fall  Free fall is the motion of a body when only the force due to gravity is acting on the body.  The acceleration on an object in free fall is called the acceleration due to gravity, or free-fall acceleration.  Free-fall acceleration is denoted with the symbols a g (generally) or g (on Earth’s surface). Section 3 Falling Objects

34. Free Fall  Free-fall acceleration is the same for all objects, regardless of mass.  Free-fall acceleration on Earth’s surface is –9.81 m/s 2 at all points in the object’s motion.  Imagine ball thrown up into the air.  Moving upward: velocity is decreasing, acceleration is – 9.81 m/s 2  Top of path: velocity is zero, acceleration is –9.81 m/s 2  Moving downward: velocity is increasing, acceleration is – 9.81 m/s 2