Dr. Jie Zou PHY 1151G 1

Welcome to PHY 1151G

Principles of Physics I

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Chapter 2

One-Dimensional Kinematics

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Outline Position Distance Displacement Velocity

Average Velocity Instantaneous Velocity

Speed Average speed Instantaneous speed

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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.

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Distance Distance = total length of travel.

SI units: meters (m). Distance is always a positive value.

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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.

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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.

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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.

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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)

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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.

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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)

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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.

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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.

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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

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Graphical Interpretation of Instantaneous Velocity

Instantaneous velocity

Instantaneous velocity = the slope of the tangent line at a given instant of time on an x vs. t graph.

t

xv

t

0lim

Tangent line at t = 1 s

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Example: Instantaneous Velocity

Qualitatively (no calculations) evaluate the instantaneous velocity at the given points on the x vs. t graph.

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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.