Week 3 Day 2: Topics Particle Model General Motion Model Constant Velocity Model Representations of Motion Motion Graphs Motion Diagrams Velocity graph to Position Answer: C Slide 1-7

Announcements: Particle Model General Motion Model Constant Velocity Model Representations of Motion Motion Graphs Motion Diagrams Velocity graph to Position Answer: C Slide 1-7

Homework Hints: Particle Model General Motion Model Constant Velocity Model Representations of Motion Motion Graphs Motion Diagrams Velocity graph to Position Answer: C Slide 1-7

General Motion and Constant Velocity Motion General Motion Model - Definitions Position Distance Displacement Average Speed Average Velocity Instantaneous Speed Instantaneous Velocity Constant v motion - Representations of motion Motion Diagram X vs. t graphs Vx vs, t graphs Describing motion in words Data table Particle Model Answer: C

Can you move? Fill in the tables for these motion events by indicating whether or not a motion event is possible.  If it is, give an example.  If not, explain why not. Displacement Final Position Possible? Example/Explanation Not 0 Average Speed Average Velocity Possible? Example/Explanation Not 0 Answer: B Slide 1-7

There and Back You and a friend decide to drive to Las Vegas, Nevada on Saturday over Labor Day weekend to go to a concert with some friends who live there. You figure you have to reach the vicinity of Las Vegas by 6 PM in order to meet your friends for dinner before the concert. It's 574 miles from UNM to the Las Vegas strip. You'd like to stop for lunch and gas bout noon. What does your average velocity need to be? It's almost all highway driving from here to Las Vegas. If you keep your speed approximately constant, what speed should your speedometer read while you are driving? After you return to UNM, what is your displacement from the time you left to go to Las Vegas? What is the total distance traveled? What is your average speed and velocity? Answer: B Slide 1-7

Making a Motion Diagram 3

Examples of Motion Diagrams 8

The Particle Model A simplifying model in which we treat the object as if all its mass were concentrated at a single point. This model helps us concentrate on the overall motion of the object. Slide 1-16

Position and Time The position of an object is located along a coordinate system. At each time t, the object is at some particular position. We are free to choose the origin of time (i.e., when t = 0). Slide 1-17

Which Way? Which way is this object moving? Is it speeding up or slowing down? How can you tell? Answer: B Slide 1-7

Motion Diagram Examples Assume speed changes occur quickly compared to time scale => will appear instantaneous Slow then Fast Fast, stop, Slow Turnaround Answer: B Slide 1-7

A. B. C. D. Checking Understanding Here is a motion diagram of a car moving along a straight stretch of road: Which of the following velocity-versus-time graphs matches this motion diagram? Answer: C A. B. C. D. Slide 2-13

Answer Here is a motion diagram of a car moving along a straight stretch of road: Which of the following velocity-versus-time graphs matches this motion diagram? Answer: C C. Slide 2-14

Where’s the train? A train is moving at a steady 30 m/s. At t = 0, the engine passes a signal light at x = 0. Without using any formulas, find the engine's position at t = 1s, 2s, and 3s. Express your reasoning in words. Slide 2-34

Where’s the train? A train is moving at a steady 30 m/s. At t = 0, the engine passes a signal light at x = 0. Without using any formulas, find the engine's position at t = 1s, 2s, and 3s. Express your reasoning in words. EQUATION FROM GRAPH EQUATION FROM AREA Slide 2-34

Checking Understanding A graph of velocity versus time for a hockey puck shot into a goal appears like so: Which of the following position graphs matches the above velocity graph? A. B. C. D. Answer: D Slide 2-21

Answer A graph of velocity versus time for a hockey puck shot into a goal appears like so: Which of the following position graphs matches the above velocity graph? Answer: D A. B. C. D. Slide 2-22

Example Problem A car moves along a straight stretch of road. The graph below shows the car’s position as a function of time. At what point (or points) do the following conditions apply? The displacement is zero. The speed is zero. The speed is increasing. The speed is decreasing. Slide 2-14

Acceleration Acceleration is: The rate of change of velocity The slope of a velocity- versus-time graph Slide 2-26

Particle Motion: The picture above is made with a stroboscope (a light that flashes at regular time intervals) made at two frames of film per second, of a ball rolling along a track. The track has a 3.0-m-long sticky section. Make a position-versus-time graph for the ball. Because you have data only at certain instants of time, your graph should consist of dots that are not connected together. What is the change in the ball’s position from t = 0 s to t = 1.0 s? c. What is the change in the ball’s position from t = 2.0 s to t = 4.0 s? d. What is the ball’s velocity before reaching the sticky section? e. What is the ball’s velocity after passing the sticky section? f. Determine the ball’s acceleration on the sticky section of the track. Answer: C Slide 1-7

Human Motion Demo - Trial 10 In each of the next four trials, you have to try to find a way to move such that you match the given representation and fill in the other two representations. (i.e. you are given a velocity vs. time graph and have to move to create the same velocity vs. time graph) Description of motion from Trial #10 Answer: C Slide 1-7