Annotate Instantaneous Velocity Problem Recall General Wolgemuthian Method: - Write the appropriate equation(s) - DO NOT substitute numbers of variables at the earliest possible time. I'm VERY serious about this. Let's discuss
- Isolate the variable you need to solve (unless it is already isolated)
*Substitute*initial conditions into equations- Show your answer
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Let's now please consider the following situation: 1) Let's say that you start at some position (we *usually* refer to that position as the origin) at time = 0.0 2) You travel 3) You then travel another 4) During the 3rd segment of your trip, you travel an additional 5) Finally you travel Construct a table of that data
Does it look like this?
Before you even start graphing that data,
Notice that CHANGING over time, it also seems to be changing at a relatively constant sorta rate which indicates a smooth curve. Something like this perhaps?Notice that I have included the original data points in light gray and an exponential - type "trend line" in red. Now please calculate the Notice that we begin by drawing a straight line to connect those to points on the curve. We'll then work to find the velocity of that straight line. Since the slope of a displacement vs time graph is velocity, we'll use that to find the AVERAGE velocity between those two points. Notice the Full Wolgemuthian ALWAYS: Initial Conditions:
Equation(s):
Isolate:
substitute:
solve:
Compare that with the velocity between 2.00 seconds and 4.00 seconds Once again we begin by drawing a straight line to connect those two points on the curve. The slope of that line will give us average velocity between those two points. There's two different errors/omissions on this graph, what are they? Notice that you are actually calculating the What's going on here? How can we have different velocities between different points?
The answer is we are calculating the AVERAGE velocity during those points. Since the velocity itself is changing (increasing) it follows that the
With that in mind, how do you suppose we find the
Notice that the Let's say we want to find the We'd start by drawing a * Now we find the slope of the tangent line. Since the point at time 3.50 seconds is also on the tangent line, the slope of the tangent line is also the value of the slope at 3.50 seconds. Since the slope of a |