How Do You Find Instantaneous Velocity at 1s?

AI Thread Summary
To find the instantaneous velocity at 1 second for an object moving along the x-axis, the position versus time graph is analyzed. The initial position is given as -2 m, and the equation of the line derived from points (0, -2) and (2, 7) is y = (7/2)x - 2. The slope, representing the average velocity over the interval from 0 to 2 seconds, is calculated as (y2 - y1)/(x2 - x1). However, the instantaneous velocity at a specific point requires the correct interpretation of the slope at that point, which may differ from the average velocity. The discussion highlights the importance of verifying calculations and understanding the distinction between average and instantaneous velocity.
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The position versus time for a certain object moving along the x-axis is shown. The object’s initial position is −2 m. Find the instantaneous velocity at 1s.
http://img23.imageshack.us/img23/5285/phy1w.jpg

Using points (0,-2) and (2,7) I found the equation of the line to be =7/2x-2. Since this is a straight line I thought the tangent line would have the same slope. So, at 1s the instantaneous velocity would be 7/2, but this is not the correct answer. Where am I going wrong?
 
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Slope of the line = (y2 - y1)/(x2 - x1).
From 0 to 2 seconds this will be the velocity of the particle.
 
Thanks for pointing out my now obvious mistake! I didn't even think to check to see if I had gotten the slope correct, I just assumed my understanding of instantaneous velocity was wrong.
 
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