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

A. B. C. D. Checking Understanding A graph of position versus time for a basketball player moving down the court appears like so: Which of the following velocity graphs matches the above position graph? Answer: C A. B. C. D. Slide 2-15

Answer A graph of position versus time for a basketball player moving down the court appears like so: Which of the following velocity graphs matches the above position graph? Answer: C C. Slide 2-16

Trials 1-6 Summary Constant velocity motion Straight line position vs. time graph Slope shows how fast you are moving Steeper Slope => faster speed Sign of Slope shows direction Velocity vs. Time Graph is flat straight line Faster => farther from time axis Above the time axis => motion in the positive direction Below the time axis => motion in the negative direction Spacing of Balloons is the same for equal time intervals Faster speed => distance between balloons increases Slide 1-7

How to describe motion What information do you need to communicate to be able to tell someone how to reproduce a motion? Frame of reference or reference frame Origin Where to start What direction to start moving What speed to start moving with Changes in direction or speed How far to go? (Where to stop) Timing Answer: C

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

Mathematical Model => symbol equation Show examples Answer: B Slide 1-7

Vectors A quantity that requires both a magnitude (or size) and a direction can be represented by a vector. Graphically, we represent a vector by an arrow. The velocity of this car is 100 m/s (magnitude) to the left (direction). This boy pushes on his friend with a force of 25 N to the right. Slide 1-32

Displacement The change in the position of an object as it moves from initial position xi to final position xf is its displacement ∆x = xf – xi. Slide 1-18

Displacement Vectors A displacement vector starts at an object’s initial position and ends at its final position. It doesn’t matter what the object did in between these two positions. In motion diagrams, the displacement vectors span successive particle positions. Slide 1-33

Reading Quiz If Sam walks 100 m to the right, then 200 m to the left, his net displacement vector points to the right. to the left. has zero length. Cannot tell without more information. Answer: B Slide 1-6

Answer If Sam walks 100 m to the right, then 200 m to the left, his net displacement vector points to the left. Answer: B Slide 1-7

Ball on Ramps (From an Exam) A ball is released from rest at the point shown on the incline and speeds up. It then rolls onto a level section of track at constant speed, and then rolls onto a second incline with the same slope as the first where it slows down. The diagram below shows the location of the ball at several instants in time. NOTE: THIS IS NOT A STROBE PHOTOGRAPH OR MOTION DIAGRAM. Describe the motion of the ball as it moves from left to right Determine the average velocity of the ball from t = 2.1 s to t = 3.6 s. Determine the average speed of the ball from t = 0.6 s to t = 5.1 s. Answer: B

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 17

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

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