How Do You Determine Instantaneous Velocity from a Tangent Line?

[webren]

Hello,
This problem is very simple, but I don't see what I am doing wrong.

"A positive-time graph for a particle moving along the x-axis is shown in Figure P2.7 Determine the instantaneous velocity at t = 2.00 s by measuring the slope of the tangent line shown in the graph."

I understand that without seeing the actual graph, it might be a little annoying, but it's a graph with a parabola with a tangent line.

My immediate reaction was to simply pick two points on the graph, and find the slope. This seems to be incorrect and seems to be the average velocity. To find the instantaneous velocity, the book uses the end points of the tangent line.

How do I go about finding the instantaneous velocity?

Thank you.

 

[Kurdt]

Simply take the gradient of the tangent line at t=0. Can be the difference of the ends of the tangent wrt the y-axis divided by the difference of the ends wrt the x axis.

 

[webren]

wrt? What is that?

 

[nrqed]

wrt? What is that?

wrt = "with respect to"

Kurdt is right but I think he made a typo, he meant "at t =2 s", not at 0 s.


If you want the instantaneous velocity at t=2 s, you draw a tangent to the x vs t graph at t=2 second and you measure the slope of the tangent line. That's all there is to it!

From what you wrote it seems like they already have drawn the tangent at 2 seconds, in which case just calculate the slope of that line (which will come out in m/s as you will notice)

Patrick

 

[d_leet]

Hello,
To find the instantaneous velocity, the book uses the end points of the tangent line.

How do I go about finding the instantaneous velocity?

Thank you.

Didn't you answer your own question? Use points of the tangent line to find the slope. This is because the slop of the tangent line at a point to any funtion is the instantaneous change in that function, if the initial funtion represents position then the slope of the tangent line at any point will represent instantaneous velocity.