Instantaneous Velocity with Position v. Time graph

In summary, the position v. time graph shows the movement of an object along the x-axis with initial position -2m. Using the formula for instantaneous velocity, the instantaneous velocity at different times can be calculated. However, there is confusion on how to properly use the formula.
  • #1
achibaby1974
1
0

Homework Statement


The position v. time graph for a certain object moving along the x-axis is shown.

I don't have the graph. Bu I have the points.

(0,-2), (1,9), (4,4), (6,4), (8,-4), (9,0)


The object's initial position is -2m. Find the instantaneous velocity at ... (m/s)
a.) 0.5s
b.) 2.5s
c.) 5 s
d.) 8.5 s


Homework Equations



I think ...

Instantaneous Velocity = (Xf - Xi) / (Tf - Ti)


The Attempt at a Solution



Well, I really don't understand where to start. Looking at the graph, for 0.5 sec ... I put 4. That was incorrect.

I put in (4-(-2)) / (0.5 - 0) = 6/0.5 = 12. That's incorrect as well.

I think I really don't understand the correct thing to do. If someone could give me some guidance or direction as how to tackle this I'd appreciate it. Thanks in advance!
 
Physics news on Phys.org
  • #2
The first thing you need to do is realize for each ordered pair (a,b) which value is position and which is time?
 
1.

What is instantaneous velocity?

Instantaneous velocity is the speed and direction of an object at a specific moment in time. It is a measure of how fast an object is moving and in what direction it is moving at a given point in time.

2.

How is instantaneous velocity calculated?

Instantaneous velocity is calculated by taking the derivative of the position function with respect to time. This means finding the slope of the position vs. time graph at a specific point in time.

3.

What is the difference between average velocity and instantaneous velocity?

Average velocity is calculated by dividing the total displacement of an object by the total time taken. It gives an overall measure of an object's speed and direction. Instantaneous velocity, on the other hand, is the speed and direction of an object at a specific moment in time.

4.

How do you interpret a position vs. time graph to determine instantaneous velocity?

On a position vs. time graph, the instantaneous velocity at a given point is represented by the slope of a tangent line drawn at that point. A steeper slope indicates a higher instantaneous velocity, while a flatter slope indicates a lower instantaneous velocity.

5.

What are some real-world applications of understanding instantaneous velocity?

Understanding instantaneous velocity is important in many fields, including physics, engineering, and sports. It can be used to analyze the motion of objects, predict the trajectory of projectiles, and improve the performance of athletes in sports such as running and swimming. It is also crucial in designing systems that require precise and accurate movements, such as robotics and manufacturing processes.

Similar threads

  • Introductory Physics Homework Help
Replies
7
Views
208
  • Introductory Physics Homework Help
Replies
5
Views
1K
  • Introductory Physics Homework Help
Replies
2
Views
1K
  • Introductory Physics Homework Help
Replies
25
Views
1K
  • Introductory Physics Homework Help
Replies
4
Views
2K
  • Introductory Physics Homework Help
Replies
7
Views
789
  • Introductory Physics Homework Help
Replies
11
Views
917
  • Introductory Physics Homework Help
Replies
13
Views
2K
  • Introductory Physics Homework Help
Replies
1
Views
2K
  • Introductory Physics Homework Help
Replies
5
Views
206
Back
Top