<p>I'm dealing with a velocity and position graph. I'm given the position graph and I need to construct the velocity graph.</p>
<p>Velocity graph:</p>
<p>y = (8/3)x if 0 < x < 3</p>
<p>y = 8 if 3 < x < 5</p>
<p>y = -(5/2)x + 20.5 if 5 < x < 9</p>
<p><em>wherever the graphs meet each other is a filled point</em></p>
<p>I need to find the position graph. Is the area under a section (under the velocity graph) represent the SLOPE of THAT particular section for the position graph?</p>
<p>For example, if there is a square on a velocity graph that has an area of 4 (when 0 < x < 2) units, would that mean that the slope of the position graph be 4 (when 0 < x < 2)?</p>
<p>How do I construct the position graph when the velocity graph has a non-zero slope (in the case of 'part' 1 and 'part' 3 of my problem above)? Do I need to find the integral?</p>
<p>So, will the first part of the velocity graph y = (8/3)x be..</p>
<p>y = (4/3) x^2?</p>
<p>and the last part of the velocity graph y = -(5/2)x + 20.5 be...</p>
<p>y = -5 x^2 + 20.5 x + c? (By the way, how do I find c in this case?)</p>
<p>For anyone who has read all of that.. I thank you muchas gracias! Any help would be much appreciated, thanks.</p>
<p>In case I'm being unclear about anything, feel free to post and ask!</p>
<p>Krabble:
Your post is a bit contradictory. It looks like you are given the velocity graph, and you need to find the position graph?</p>
<p>The area under the velocity graph represents the total distance covered (or 'total position'). Strictly speaking, the total area between t=t1 and t=t2 represents the change in 'total position' value from t1 to t2. </p>
<p>The slope of the position graph at any time t is just the value of the velocity graph at that time. In your example, if velocity=2 for 0 <= t < =2, the area under the velocity graph from t=0 to t=2 would be 4 i.e. total distance travelled from t=0 to t=2 would be 4 units. However, the slope of the position graph over this time interval would be the velocity - in this case, a constant value of 2.</p>
<p>To avoid confusion, I'd suggest not using the same variable 'y' to represent both velocity and position; use v(t) and s(t) instead, for example. You're right - the indefinite integrals of v(t) will give you the position graph in each of those different time intervals. There is no way to tell what the 'c' will be for the position graph, if all you are given is v(t). Without further info, I would assume c=0 .</p>