Chapter 2: Reference Frames, Diplacement, and Velocity Sections 2-1 to 2-3 Pages 20-23

Key Formulas

2-1 Reference Frames and Displacement Any measurement of position, distance, or speed must be made with respect to a reference frame. For example, if you are sitting on a train and someone walks down the aisle, their speed with respect to the train is a few miles per hour, at most. Their speed with respect to the ground is much higher. © 2014 Pearson Education, Inc.

2-1 Reference Frames and Displacement Motion is described in many ways: Distance Velocity Displacement Acceleration Speed Direction But ALL of this depends on your point of view, or frame of reference. © 2014 Pearson Education, Inc.

2-1 Reference Frames and Displacement When we describe motion, it is important to not only describe its speed, but also its direction. We can always choose to place the origin (0,0) and the x & y axes as we’d like However, we usually choose +x to the right and –x to the left. © 2014 Pearson Education, Inc.

2-1 Reference Frames and Displacement The displacement is written: ∆x = x2 − x1 Left: Displacement is positive. Right: Displacement is negative. © 2014 Pearson Education, Inc.

2-1 Reference Frames and Displacement We make a distinction between distance and displacement. Displacement (blue line) is how far the object is from its starting point, regardless of how it got there. Distance traveled (dashed line) is measured along the actual path. © 2014 Pearson Education, Inc.

2-1 Reference Frames and Displacement What distance has been traveled? What is the displacement? © 2014 Pearson Education, Inc.

2-1 Reference Frames and Displacement Question: If you go to get a drink during class, what is the distance that you’ve traveled? What is your displacement?

2-1 Reference Frames and Displacement Since displacement has both magnitude (number) and direction, it is represented by a vector: A vector is shown as an arrow.

2-1 Reference Frames and Displacement Figure 2 Figure 1 Determine the displacement for each Figure: Figure 1: Figure 2:

2-2 Average Velocity Speed: how far an object travels in a given time interval Velocity includes directional information: (2-1) © 2014 Pearson Education, Inc.

2-2 Average Velocity Velocity tells us both magnitude (numerical value) and direction (+ or -): So…..Velocity is a VECTOR!! © 2014 Pearson Education, Inc.

2-2 Average Velocity Let’s look at the example from earlier: Determine the speed: © 2014 Pearson Education, Inc.

2-2 Average Velocity Let’s look at the example from earlier: Determine the velocity: © 2014 Pearson Education, Inc.

2-2 Average Velocity So, average velocity is calculate: © 2014 Pearson Education, Inc.

2-2 Average Velocity Example Problem: During a 3.00 s time interval, the runner’s position changes from x1 = 30.0 m to x2 = 10.0 m. What was the runner’s average velocity? © 2014 Pearson Education, Inc.

2-2 Average Velocity Video Problem: Determine the average velocity of the runner up the hill. https://serc.carleton.edu/student_videos/index.html © 2014 Pearson Education, Inc.

2-3 Instantaneous Velocity The instantaneous velocity is the average velocity, in the limit as the time interval becomes infinitesimally short. These graphs show (a) constant velocity and (b) varying velocity. (2-3) © 2014 Pearson Education, Inc.

2-3 Instantaneous Velocity Instantaneous speed always equals instantaneous velocity (apart from direction) since when time is infinitesimally small, distance = displacement.