Determining instantaneous velocity from a graph

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Homework Help Overview

The problem involves determining the instantaneous velocity of a rabbit moving through a straight tunnel, based on a provided position-time graph. The specific time of interest is 32.5 seconds.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss various numerical attempts to estimate the instantaneous velocity, with values derived from the graph. There is a suggestion to draw a tangent line at the specified time to find the slope, which represents the instantaneous velocity.

Discussion Status

Participants are actively exploring different methods to estimate the instantaneous velocity. Some have provided numerical estimates based on their interpretations of the graph, while others are clarifying the method of drawing a tangent line to determine the slope. There is no explicit consensus on the final value yet.

Contextual Notes

Participants note that the quality of the graph may hinder accurate calculations, as it was originally intended for a different problem. There are also discussions about the precision of the values obtained and the appropriateness of the tangent line's placement.

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Homework Statement


This is how my problem has been presented:
The position of a rabbit along a straight tunnel as a function of time is plotted in Fig. 2-26.

http://img134.imageshack.us/img134/8263/graphxt5.th.jpg http://g.imageshack.us/thpix.php

Determine its instantaneous velocity at the following times.

(b) t = 32.5 s

2. The attempt at a solution

Attempts are:
0.49231 m/s
0.50769 m/s
0.523077 m/s
0.53846 m/s
0.553846 m/s
0.56923 m/s
0.57085 m/s
0.5846 m/s

The numbers are obtained, though rounded, for x/32.5 s, where x is, and in order:
16
16.5
17
17.5
18
18.5
18.552625 (obtained by count pixels and some math to get a number, though it failed)
19

The problem is probably just because the graph is terrible for this kind of work, due to the fact that the graph came off some different problem that was intended for students to describe the graph, so the numbers aren't very well set.

These are the numbers I obtained off the few weeks of physics I had but any other input is fine.
Its also fine to give a guess off the top of your head, so i can try it, but please base it off something.
 
Last edited by a moderator:
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To find instentanious velocity just draw a tangent to the graph at that specific time and calculate the tangents slope
 
So just to be sure, it would be a line from a point (I used 0,0) through tangent to the point at 32.5s (which would be the middle of the line, since it is about 5 pixels wide).

Also that it would look like this picture, more or less.

http://img515.imageshack.us/img515/2900/graph2mg6.th.jpg http://g.imageshack.us/thpix.php

If so, then I do get a new number, 0.57143 m/s at 18.57 m.

Thanks for your input.
 
Last edited by a moderator:
Yes that would roughly be it. However I think the tangent line should be a bit higher.
 

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