# Finding X components for instantaneous velocity with points on a graph

• NEAnderson90
In summary, the conversation discusses a test car traveling along the x-axis and a graph showing its position as a function of time. The task is to find the x-component of instantaneous velocity at points A-G on the graph. The person asking the question is unsure about how to approach the problem and is seeking clarification on determining the magnitude of velocity and finding the x-component from it.
NEAnderson90
A test car travels in a straight line along the axis. The graph in the figure shows the car's position as a function of time. (attached figure)
Find the x component of instantaneous velocity at points A-G.

Could someone please tell me how I'm supposed to go about this problem? I know C and G are zero, but I don't know why.

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Hi, welcome to PF.Let me check what you already know:

- So how do you determine the magnitude of the velocity from a time-distance graph?
- How do you get the x-component from the magnitude of the velocity in this case?

If you can answer both these questions you should be able to do the question, unless there are any surprises on the (as yet invisible) image.

I would approach this problem by first understanding the concept of instantaneous velocity. Instantaneous velocity is the rate of change of an object's position at a specific moment in time. In this case, the x component of instantaneous velocity refers to the horizontal component of the car's velocity.

To find the x component of instantaneous velocity at points A-G, we can use the slope formula: velocity = (change in position)/(change in time). This means that the x component of instantaneous velocity is equal to the change in x position divided by the change in time.

At point A, the x position is 0 and the time is 0, so the velocity is also 0. This is because the car has not yet started moving at this point.

At point B, the x position is 5 and the time is 1, so the velocity is (5-0)/(1-0) = 5 units/time. This means that at this point, the car is moving horizontally at a rate of 5 units per time.

At point C, the x position is 10 and the time is 2, so the velocity is (10-5)/(2-1) = 5 units/time. This is the same as the velocity at point B because the car is moving at a constant speed.

At point D, the x position is 15 and the time is 3, so the velocity is (15-10)/(3-2) = 5 units/time. Again, this is the same as the velocity at points B and C because the car is still moving at a constant speed.

At point E, the x position is 20 and the time is 4, so the velocity is (20-15)/(4-3) = 5 units/time. This pattern continues for points F and G, where the velocity remains constant at 5 units/time.

To summarize, the x component of instantaneous velocity at points A-G is 0 at points A and G because the car is not moving horizontally at these points. At points B-F, the x component of instantaneous velocity is 5 units/time because the car is moving horizontally at a constant speed of 5 units per time.

## 1. How do you find the X components for instantaneous velocity with points on a graph?

The X components for instantaneous velocity can be found by using the slope formula, which is (change in Y)/(change in X). This will give you the average velocity between two points on the graph. To find the instantaneous velocity, you will need to take the limit of this formula as the change in time approaches zero.

## 2. Can you explain the difference between average velocity and instantaneous velocity?

Average velocity is the total displacement divided by the total time. It gives an overall average of the velocity between two points on a graph. Instantaneous velocity, on the other hand, is the velocity at a specific moment in time. It is calculated by taking the limit of the average velocity formula as the change in time approaches zero.

## 3. How can I determine the X components of instantaneous velocity if I only have a position vs. time graph?

If you only have a position vs. time graph, you can still find the X components of instantaneous velocity by finding the slope of the tangent line at a specific point on the graph. The slope of the tangent line will give you the instantaneous velocity at that point. This process can be repeated for multiple points on the graph to get a better understanding of the velocity at different points in time.

## 4. What is the significance of finding the X components of instantaneous velocity?

The X components of instantaneous velocity can provide important information about the motion of an object. It can show how quickly an object is moving at a specific moment in time and in which direction. This information can be used to calculate other important quantities such as acceleration and displacement.

## 5. Are there any limitations to finding the X components of instantaneous velocity with points on a graph?

One limitation to this method is that it only gives the instantaneous velocity at specific points on the graph. It does not show the velocity at any other points in time. Additionally, this method assumes that the motion of the object is continuous and smooth, which may not always be the case in real-world situations.

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