Instantaneous Velocity Problem

In summary, the conversation discusses how to find the instantaneous velocity of a particle moving along the x-axis based on a given positive-time graph. The suggested method is to draw a tangent line at the desired point and measure its slope. The difference between using two points on the graph and the end points of the tangent line is also clarified. The concept of wrt (with respect to) is also briefly mentioned.
  • #1
webren
34
0
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.
 
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  • #2
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.
 
  • #3
wrt? What is that?
 
  • #4
webren said:
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
 
  • #5
webren said:
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.
 

1. What is instantaneous velocity?

Instantaneous velocity is the rate of change of an object's position at a specific moment in time. It is the velocity of an object at a specific point along its path, as opposed to the average velocity over a period of time.

2. How is instantaneous velocity different from average velocity?

Average velocity is calculated by dividing the total displacement of an object by the total time it took to cover that distance. Instantaneous velocity, on the other hand, is the velocity at a specific moment in time and can vary throughout an object's motion.

3. How is instantaneous velocity calculated?

Instantaneous velocity is calculated by taking the derivative of an object's position function with respect to time. In other words, it is the slope of the tangent line to the position-time graph at a specific point.

4. Why is instantaneous velocity important in physics?

Instantaneous velocity is important because it allows us to analyze an object's motion at a specific moment in time. It is also used in determining an object's acceleration, which is a crucial parameter in understanding the forces acting on an object.

5. Can instantaneous velocity be negative?

Yes, instantaneous velocity can be negative. Negative instantaneous velocity indicates that an object is moving in the opposite direction of its positive velocity. This can happen when an object changes direction or experiences deceleration.

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