Finding Instantaneous Velocity

In summary, the conversation discusses finding the instantaneous velocity at a specific time for an object moving along the x-axis. The initial position of the object is -2 m and using the points (0,-2) and (2,7), the equation of the line is found to be 7/2x-2. However, it is noted that the slope of the line is not the correct answer for the instantaneous velocity at 1s. Upon further examination, it is discovered that the slope was incorrectly calculated.
  • #1
hackett5
9
0
The position versus time for a certain object moving along the x-axis is shown. The object’s initial position is −2 m. Find the instantaneous velocity at 1s.
http://img23.imageshack.us/img23/5285/phy1w.jpg [Broken]

Using points (0,-2) and (2,7) I found the equation of the line to be =7/2x-2. Since this is a straight line I thought the tangent line would have the same slope. So, at 1s the instantaneous velocity would be 7/2, but this is not the correct answer. Where am I going wrong?
 
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  • #2
Slope of the line = (y2 - y1)/(x2 - x1).
From 0 to 2 seconds this will be the velocity of the particle.
 
  • #3
Thanks for pointing out my now obvious mistake! I didn't even think to check to see if I had gotten the slope correct, I just assumed my understanding of instantaneous velocity was wrong.
 

What is instantaneous velocity?

Instantaneous velocity is the velocity of an object at a specific moment in time. It is the rate of change of an object's position with respect to time, and can be calculated by finding the slope of the tangent line to the object's position-time graph at that particular moment.

Why is instantaneous velocity important?

Instantaneous velocity is important because it allows us to understand the motion of an object at a particular moment in time. It can help us determine how fast and in which direction an object is moving, and it is a crucial concept in the study of kinematics and dynamics.

How is instantaneous velocity different from average velocity?

Instantaneous velocity is the velocity at a specific moment in time, while average velocity is the total displacement divided by the total time. Average velocity gives us an overall measure of an object's motion, while instantaneous velocity gives us a more precise understanding of its motion at a single point.

What factors can affect the instantaneous velocity of an object?

The instantaneous velocity of an object can be affected by several factors, including the object's initial velocity, acceleration, and any external forces acting on it. Other factors such as air resistance and friction can also impact an object's instantaneous velocity.

How can we calculate instantaneous velocity?

To calculate instantaneous velocity, we can use the formula v = Δx/Δt, where v is the instantaneous velocity, Δx is the change in position, and Δt is the change in time. We can also use the derivative of an object's position function with respect to time to find the instantaneous velocity at a specific point.

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