(10) 7. Great! If you've completed this section you now have found the velocity two ways. If these do not appear as numbers, then you have not completed all of the previous questions. - Using an equation $$ v_{ ext {average, }}=\frac{\Delta x}{\Delta t} $$ you got $$ 127.55 \mathrm{~cm} / \mathrm{s} $$. - Using the slope of the position vs time graph you got: Student Response $$ \mathrm{cm} / \mathrm{s} $$ A student makes the following claim: The slope of a position vs. time graph for an object and that object's äverage velocity are the same thing. Do you agree or disagree? Explain your reasoning below. Think about your velocity results from Part 1 and Part 2 . Discuss the units of the slope vs. the units of the average velocity as well as the similarity in their values to support your reasoning.

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(10) 7. Great! If you've completed this section you now have found the velocity two ways. If these do not appear as numbers, then you have not completed all of the previous questions. - Using an equation $$ v_{	ext {average, }}=\frac{\Delta x}{\Delta t} $$ you got $$ 127.55 \mathrm{~cm} / \mathrm{s} $$. - Using the slope of the position vs time graph you got: Student Response $$ \mathrm{cm} / \mathrm{s} $$ A student makes the following claim: The slope of a position vs. time graph for an object and that object's äverage velocity are the same thing. Do you agree or disagree? Explain your reasoning below. Think about your velocity results from Part 1 and Part 2 . Discuss the units of the slope vs. the units of the average velocity as well as the similarity in their values to support your reasoning.

UpStudy AI · Accepted Answer

1. The average velocity is defined as  
   $$
   v_{\text{avg}} = \frac{\Delta x}{\Delta t}.
   $$

2. When you plot position versus time, the slope of that line is calculated as  
   $$
   \text{slope} = \frac{\Delta x}{\Delta t},
   $$  
   which has the same units as average velocity, namely centimeters per second (cm/s).

3. In the specific case described, you obtained an average velocity of  
   $$
   127.55\ \text{cm/s}
   $$  
   using the equation and found a matching value using the slope from the graph. This shows that in this context the slope of the position vs. time graph is numerically equivalent to the average velocity.

4. However, it is important to note that this equivalence holds when the position vs. time graph is a straight line (or nearly so), meaning that the velocity is constant during the time interval under consideration. In situations where the object’s motion is non-uniform (i.e., the graph is curved), the slope of the tangent at a specific point gives the instantaneous velocity, which is not the same as the average velocity over an interval.

5. Therefore, I agree with the student’s claim in the context of this experiment where the motion appears uniform, and the graph is approximately linear. The units and numerical similarity confirm that the slope, calculated as $$\Delta x/\Delta t$$, represents the average velocity for the measured interval.
I agree with the student's claim. In this case, since the position vs. time graph is straight, the slope equals the average velocity of 127.55 cm/s. The units for both are the same (cm/s), and their values match, confirming that the slope and average velocity are the same when the motion is uniform.

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