Why does the slope of a PT Graph equal the VT graph?

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SUMMARY

The slope of a Position-Time (PT) graph directly represents velocity, which is defined as the change in position over time. In mathematical terms, the slope is calculated as ΔY/ΔX, where ΔY is the change in position (measured in meters) and ΔX is the change in time (measured in seconds). Thus, the slope of the PT graph equals the Velocity-Time (VT) graph, confirming that velocity is the rate of change of position with respect to time.

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Can someone please explain this to me (please see title)? I understand how to compute it but why is this so?

Thanks
 
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You mean momentum-time graph and velocity-time graph?
 
or is it the pressure-temperature and volume-temperature graph for ideal gases?
 
I mean Position-Time and Velocity-Time.
 
What does slope mean?

Slope = \frac{\Delta Y}{\Delta X}

What is your Y-axis? position (meters)
What is your X-axis? time (seconds)

Therefore,

Slope = position/time = meters/seconds = velocity

Velocity is the change of rate of change of position per unit time.
 

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