1. Principles of Physics I
Welcome to PHY 1151G
Principles of Physics I
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2. One-Dimensional Kinematics
Chapter 2
One-Dimensional Kinematics
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3. Outline Position Distance Displacement Velocity Speed Average Velocity
Instantaneous Velocity
Speed
Average speed
Instantaneous speed
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4. 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

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

6. 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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Dr. Jie Zou PHY 1151G

7. 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

8. 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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Dr. Jie Zou PHY 1151G

9. 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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Dr. Jie Zou PHY 1151G

10. 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

11. 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) m/s; (c) 0)
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Dr. Jie Zou PHY 1151G

12. 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

13. 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

14. 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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15. 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
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16. Example: Instantaneous Velocity
Qualitatively (no calculations) evaluate the instantaneous velocity at the given points on the x vs. t graph.
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17. 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