I was wondering if someone could explain the relationships between the three motion graphs (Position-Time, Velocity-Time, and Acceleration-Time). I believe that the slope of the P-T is Velocity and the slope of the V-T is Acceleration. I just want to know how they all relate to each other, and how you can find different kinematic variables using each graph.
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Yes, that's correct. The slope of any function (position, velocity, acceleration, number of bananas, etc) plotted along the time axis is the rate of change of that function. If your graph is a straight line, it's easy to find the slope, which is just rise/run, e.g.
$$ \text{velocity} = v = \frac{\Delta x}{\Delta t} = \frac{\text{(change in position)}}{\text{(change in time)}}. $$
To find position from velocity on the other hand (or velocity from acceleration), you need the area under the velocity (or acceleration) versus time graph, since
$$ \Delta x = v\Delta t. $$
When your graph is not a straight line, the slope is changing (and areas will be harder to calculate), but the same principle holds in terms of limits, with $\Delta x\rightarrow 0$, $\Delta t\rightarrow 0$. This is where calculus comes in, with slope given by the derivative and area by the integral.
