1. May 24, 2004

### Marcules

Hello,
I have this velocity v. time parabola graph (which i attached to this post) and what I am suppose to make an acceleration v. time graph from it. Its tuff to see but there are specific little points on the curve that were plotted. the velocity isn't constant which probably means I have to find the instantanous acceleration at each point. I'm suppose to use tangent lines(I think) and I'm a little confused on what they are exactly. My best guess is that tangent lines are lines used just to find the slope. What I'm thinking is that I make a line between two points on my graph and calculate the slope, right? So all I have to do is find the slope between every set of points on my velocity v. time graph and then plot my acceleration v. time graph from these slopes I found? I also have to describe the acceleration which I'm pretty sure will be easy once I finish this graph. Please take a look and see if you have the answer to my question. Thanks for your time.......

Last edited by a moderator: Apr 25, 2011
2. May 24, 2004

### HallsofIvy

Staff Emeritus
The important thing is that you have the answer to this question!

First the "tangent" line is not a line between two points on a graph- that's a "secant". The tangent line to a graph is exactly like a tangent to a circle. It touches the graph at one point and has the same direction as the graph at that point.

There is no way to draw a tangent line just by connecting two points- that's why we need calculus in the first place. With a problem like this it may be enough to "eyeball" it- draw your line to "skim" the graph at each point. A more accurate way is to use a small mirror. Place the mirror on the graph at the point at which you want to draw the tangent. Turn the mirror until it appears that the graph goes "smoothly" into the mirror (no sudden angle at the mirror) and use the mirror itself as a straight edge to draw a line. That line will be perpendicular to the graph. Now use the mirror in the same way to draw the perpendicular to that line, still holding the mirror at the original point. This line will be tangent to the graph.