Online assignment E.2.4. Interpreting Motion with Graphs

You've seen in the online review and exercises for Chapter 2 that motion can be represented in position vs. time and velocity vs. time graphs. This is a common and important way to study motion, and you need to be able to draw, apply, and interpret such graphs. In this assessment, you'll apply the following fundamental principles in interpreting motion graphs. But first, a note about IWP.

Tech Tip About IWP

For the next assignment and many more throughout the year, you'll be using applets, many of which allow interaction. Most of the applets we'll be using were authored using Interactive Web Physics (IWP), a software system created at NCSSM by Taylor Brockman. Several NCSSM students and alumni have participated in the development of the software. Brockman, who graduated from NCSSM in 1999, went on to help found Motricity, now Voltari, with classmate, Judd Bowman.

Java is required to run IWP. By this time, you should have Java working on your computer. Different versions of the IWP Tutorial are given below depending on how you prefer to view it. These tutorials are also available from the IWP item in the course menu at the top. We recommend you view one of the video tutorials for a quick introduction to how to use IWP. Then you can move on to the next assignment.

Tutorial

Here are a few pointers about IWP animations:

  • When you click on a link to open an animation, you may be prompted with a challenge box asking whether you want to allow or deny the applet to run. In that case, select allow. Some browsers may ask if want the applet components to be blocked. In this case, answer no.
  • Depending on the speed of your computer, you may see momentary interruptions in motions that are intended to be smooth.

So much for the technology. Now for some important points about the physics.

Important note Fundamentals of Motion Graphs

  1. The slope of a position vs. time graph is the instantaneous velocity. In mathematical terms, the limit of the ratio Δx/Δt as Δt approaches 0 is the instantaneous velocity, v.

  2. The slope of a velocity vs. time graph is the instantaneous acceleration. In mathematical terms, the limit of the ratio Δv/Δt as Δt approaches 0 is the instantaneous acceleration, a.

  3. For any two points on a position vs. time graph, the change in the position coordinates, Δx, divided by the change in the time coordinates, Δt, is the average velocity; that is, vav = Δx/Δt.

  4. For any two points on a velocity vs. time graph, the change in the velocity coordinates, Δv, divided by the change in the time coordinates, Δt, is the average acceleration; that is, aav = Δv/Δt.

  5. The area under the line on a graph of velocity vs. time is the displacement.

Application of fundamentals 1 and 2 leads to the most common situations. By the way, there's no need to memorize the following. If you know and understand the fundamentals, then you can apply them.

Important note Applying the Fundamentals

  1. The position vs. time graph of an object that isn't moving is a horizontal line.

  2. The position vs. time graph of an object traveling with constant velocity is a straight line. The slope of the line is positive (negative) if the velocity is positive (negative).

  3. The velocity vs. time graph of an object traveling with constant velocity is a horizontal line.

  4. The velocity vs. time graph of an object traveling with constant acceleration is a straight line. The slope of the line is positive (negative) if the acceleration is positive (negative).

  5. The position vs. time graph of an object traveling with constant acceleration is a curved line. (The mathematical function is a parabola.) The slope of the curve increases (decreases) with time if the velocity is becoming more positive (negative).

The language of physics is supposed to be precise, and it usually is. But there are some word usages that can be confusing. That's because they have a strict meaning in physics, but they may have a different meaning in common, everyday usage. Sometimes, these usages even get confused in physics textbooks or when we talk to each other in physics classes. So we have to be on guard for such situations. Here's one that relates to the current subject.

Important note Average speed is total distance traveled divided by the total time to travel that distance. Average speed is not the magnitude of the average velocity. Here's an example to illustrate.

Problem: You travel 25 miles north along a straight road in 0.50 hr. Then you turn around and travel 15 miles in the opposite direction in 0.25 hr. Give the following: a) your average velocity for the entire trip, b) the magnitude of your average velocity for the entire trip, c) your average speed for the entire trip.

Solution:

  1. The average velocity is the displacement divided by the total time. The displacement is 10 miles north, so the average velocity is (10 miles north) / (0.75 hr) = 13 mi/hr north.

  2. The magnitude of the average velocity is 13 mi/hr.

  3. The average speed is the total distance traveled, 40 miles, divided by the total time, 0.75 hr. This equals 53 mi/hr.

With these things in mind, go on to WebAssign assessment E.2.4.


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