Calculating acceleration from 2 tangent lines

AI Thread Summary
To calculate acceleration from two tangent lines on a position vs. time graph, the slopes of the tangents represent the velocities at specific points. The average acceleration can be determined by subtracting the initial velocity from the final velocity and dividing by the time interval between the two points. Even if the tangent points do not correspond to the overall initial and final times, acceleration can still be computed over the chosen interval. It is important to note that if acceleration is constant, this method remains valid. Thus, the average acceleration can be calculated without needing to reference the overall initial and final times.
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I have a position vs. time graph which is slightly curved. I found the slope of 2 tangent lines which I know are the velocity. My question is how do I get the acceleration using these 2 slopes. One slope is 295cm/s and the other is 575cm/s. I know that avg acceleration is final velocity - initial velocity/ final time - initial time but because these points aren't at the initial and final times, I don't think I can use that.
 
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Then don't use final time in the acceleration equation! If acceleration is a constant, you can calculate it over any time interval.
 

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