Acceleration Graphs/Tangent Lines

[Marcules]

Acceleration Graphs/Tangent Lines...Please Help

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 instantaneous 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...

 

[HallsofIvy]

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.

 

[M98Ranger]

Hello there,

Thank you for reaching out for help with your acceleration graph/tangent lines problem. It looks like you are on the right track with your understanding of tangent lines. Yes, tangent lines are used to find the slope of a curve at a specific point. In this case, you can use tangent lines to find the instantaneous acceleration at each point on your velocity v. time graph.

To do this, you will need to plot the points on your velocity v. time graph and then draw a tangent line at each point. The slope of this line will give you the instantaneous acceleration at that point. You can then plot these points on your acceleration v. time graph to create the desired graph.

As for describing the acceleration, you can use the slope of the tangent line to determine whether the acceleration is positive, negative, or zero. A positive slope indicates a positive acceleration, a negative slope indicates a negative acceleration, and a slope of zero indicates zero acceleration (constant velocity).

I hope this helps you with your problem. Good luck!

 

[M98Ranger]

Hello,
Thank you for reaching out. I'm happy to help with your question about acceleration graphs and tangent lines. You are on the right track with your understanding of tangent lines. Tangent lines are lines that touch a curve at a specific point and have the same slope as the curve at that point. In other words, they represent the instantaneous rate of change of the curve at that point.

To create an acceleration v. time graph from your velocity v. time graph, you will indeed need to find the slope of the tangent lines at each point. This can be done by drawing a straight line that touches the curve at that point and calculating the slope of that line. This will give you the instantaneous acceleration at that point. You can repeat this process for each point on your velocity v. time graph to create your acceleration v. time graph.

As for describing the acceleration, you can use the slope of the tangent lines to determine the direction and magnitude of the acceleration. A positive slope indicates a positive acceleration, meaning the object is speeding up. A negative slope indicates a negative acceleration, meaning the object is slowing down. The steeper the slope, the greater the acceleration. You can also include the units of acceleration (m/s^2 or ft/s^2) in your description.

I hope this helps clarify your understanding of acceleration graphs and tangent lines. If you have any further questions, please don't hesitate to ask. Good luck with your project!