Motion in One Dimension: Displacement and Velocity

1. Motion in One Dimension:Displacement and Velocity Chapter 2: Section 1

2. Learning Targets • 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 vs. time P2.1A, P2.1C, P2.1D, P2.2A, P2.3a

3. Scalar vs. Vector Quantities • Most of the quantities encountered in physics are either scalar or vector quantities

4. Scalar Quantities • Scalar quantities are represented by a magnitude alone. • Does not indicate direction • Examples: time, distance, speed, temperature, and volume • 4 m, 3 seconds, 20 cm3

5. Vector Quantities • Vector quantities are represented by both a magnitude and a direction. • Answers how much and where it is going • Example: moving east at 100 km/h

6. One Dimensional Motion • The simplest form of motion • Example: a commuter train on a straight track • The train can move only forward or backwards; not left to right or up and down

7. Distance vs. Displacement • Distance tells you the total amount of ground covered • Distance is a scalar quantity • Displacement is the overall change in position of an object from its initial position to its final position • Displacement is a vector quantity

8. Yellow Line = Distance • Green Line = Displacement

9. If a gecko runs from left to right along a stick marked in centimeters it moves from an initial position (Xi), to a final position (Xf) • In this case the gecko’s distance and displacement are equal

10. Displacement = Final Pos’n - Initial Pos’n ∆X = Xf - Xi • If the gecko runs up a tree, the measuring stick would serve as the y-axis • The gecko’s position would be written as ∆Y

11. Displacement does not always tell you the distance an object has moved • Example: A gecko runs up a tree from the 20cm mark to the 80cm mark. It then moves down the tree to the 50 cm mark. • It has traveled a total distance of 90 cm. (Scalar) • Its displacement is 30 cm upward. (Vector) • What is the gecko’s displacement if it returns to its initial position?

12. Positive vs. Negative displacement • In one dimensional motion, there are only two directions that an object can move • These directions can be described as positive or negative • In general, right (or east) is considered positive while left (or west) is considered negative • Similarly, upward (or north) will be considered positive and downward (or south) will be considered negative

13. Relative Motion • All motion depends upon a frame of reference • Choosing a frame of reference allows you to measure the change in an object’s position relative to a stationary object • Any frame of reference can be chosen as long as it remains fixed • Ex: A train moving past a station

14. What are some other examples where frame of reference would have an effect on your view of relative motion?

15. Velocity • Knowing how fast an object is traveling is also important when evaluating motion • Velocity is a vector quantity that measures the rate and direction of the object’s change in position

16. Average Velocity • Consider a car moving along a highway in a straight line (x-axis). • Suppose a car drives from point A to point B down a highway (x) in a specific time interval (t)

17. Calculating Average Velocity • The average velocity, vavg, is defined as the displacement (∆X) divided by the time interval during which the displacement occurred. • Measured in meters per second (m/s) avg. velocity = change in position / change in time vavg = ∆X / ∆t

18. Average velocity can be positive or negative, depending on the sign of the displacement • The time interval is always positive • If you drive 370 km west along a straight highway and it takes from 10 am to 3 pm, what is your avg. velocity in km/h?

19. Velocity vs. Speed • Velocity describes motion with both a direction and a magnitude • Speed has no direction, only magnitude • An object’s average speed is equal to the distance traveled divided by the time interval for the motion Average speed = distance traveled/time of travel Speedavg= ∆d / ∆t

20. Graphing Velocity • For a position-time graph, the average velocity can be determined by calculating the slope of the line between any two points • On a position-time graph, a positive slope indicates a positive velocity, a negative slope indicates a negative velocity, and a zero slope is at rest (no change in position)

21. Using the position-time graph below, describe the motion and calculate the average velocity for a bicyclist traveling East/West