Principles of Physics I Welcome to PHY 1151G Principles of Physics I Dr. Jie Zou PHY 1151G

One-Dimensional Kinematics Chapter 2 One-Dimensional Kinematics Dr. Jie Zou PHY 1151G

Outline Position Distance Displacement Velocity Speed Average Velocity Instantaneous Velocity Speed Average speed Instantaneous speed Dr. Jie Zou PHY 1151G

Position Position: the first step in describing the motion of particle is to set up a coordinate system that defines positions. (I) Set up the x axis; (II) Choose a point as the origin, x=0; (III) Choose a positive direction. Dr. Jie Zou PHY 1151G

Distance Distance = total length of travel. SI units: meters (m). Distance is always a positive value. Dr. Jie Zou PHY 1151G

Example: Distance Suppose that you leave your house, drive to the grocery store, and then return home. The distance you have covered in your trip is 8.6 mi. © 2010 Pearson Education, Inc. Dr. Jie Zou PHY 1151G

Displacement Displacement: change in position (final position - initial position). In one-dimensional motion: x = xf - xi. SI units: meters (m). Displacement can be positive, negative or zero. The signs indicate the direction of the displacement. Displacement and distance are quite different. Dr. Jie Zou PHY 1151G

Active Example 2-1: Find the Distance and Displacement Calculate (a) the distance and (b) the displacement for a trip from your friend’s house to the grocery store and then to your house (Answer: (a) d = 10.7 mi; (b) x = 2.1 mi). Note: As a general rule, include steps when working out a physics problem. © 2010 Pearson Education, Inc. Dr. Jie Zou PHY 1151G

Average Speed Average speed = distance/elapsed time. SI units: meters per second (m/s). Average speed is always positive. Conceptual Checkpoint 2-1 Average Speed: You drive 4.00 mi at 30.0 mi/h and then another 4.00 mi at 50.0 mi/h. What is your average speed? (Answer: 37.6 mi/h < 40.0 mi/h) © 2010 Pearson Education, Inc. Dr. Jie Zou PHY 1151G

Average Velocity Average velocity: The object’s displacement x divided by the time interval t during which that displacement occurs. vav = displacement/time interval = x/t = (xf – xi )/t. SI unit: meters per second (m/s). The average velocity can be positive, negative, or zero. The signs indicate direction. Average velocity gives more information than average speed. It tells us on average how fast and in which direction the object is moving. Dr. Jie Zou PHY 1151G

Example 2-2: Sprint Training An athlete sprints 50.0 m in 8.00 s, then stops, and walks slowly back to the starting line in 40.0 s. If the “sprint direction” is taken to be positive, what is (a) the average sprint velocity (b) the average walking velocity (c) the average velocity for the complete round trip? (Answer: (a) 6.25 m/s; (b) -1.25 m/s; (c) 0) © 2010 Pearson Education, Inc. Dr. Jie Zou PHY 1151G

Graphical Interpretation of Average Velocity Position-time graph (x vs. t curve): a sketch of how position changes as a function of time. Average velocity during a given time interval = the slope of a line connecting the two points on an x vs. t graph. Dr. Jie Zou PHY 1151G

Example: Plot x vs. t Graph and Find Average Velocity Suppose that you drive in a straight line at 10 m/s for 2 minutes, then you stop for 5 minutes, and finally you drive at 15 m/s for another 3 minutes. (a) Plot x vs. t graph for your motion from t = 0 to t = 10 s. (b) Use plot from (a) to find the average velocity between t = 0 and t = 10 s. For answers, see class discussion. Dr. Jie Zou PHY 1151G

Instantaneous Velocity Instantaneous velocity: The velocity of an object at any instant of time SI units: meters per second (m/s). The instantaneous velocity can be positive, negative, or zero. The signs indicate direction. When velocity is constant, the average velocity over any time interval is = the instantaneous velocity at any time. Instantaneous speed: The magnitude of the instantaneous velocity. Instantaneous speed is always positive or zero. Speedometer Dr. Jie Zou PHY 1151G

Graphical Interpretation of Instantaneous Velocity Instantaneous velocity = the slope of the tangent line at a given instant of time on an x vs. t graph. Tangent line at t = 1 s Dr. Jie Zou PHY 1151G

Example: Instantaneous Velocity Qualitatively (no calculations) evaluate the instantaneous velocity at the given points on the x vs. t graph. Dr. Jie Zou PHY 1151G

Homework See online homework assignment at www.masteringphysics.com Note: the Title of the assignment has the format of “PHY 1151 mm/dd/yy”; “mm/dd/yy” indicates the date when the homework is assigned. Dr. Jie Zou PHY 1151G