Advanced Functions Average vs. Instantaneous velocity

In summary, the conversation discusses the concept of average velocity on very short time intervals and the potential relationship between this type of velocity and instantaneous velocity. It also raises the question of whether it is possible to accurately define velocity at a specific interval.
  • #1
Wild ownz al
30
0
What do the average velocities on the very short time intervals [2,2.01] and [1.99,2] approximate? What relationship does this suggest exist between a velocity on an interval [a,b] and a velocity near t=a+b/2 for this type of polynomial?
 
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  • #2
That looks very much like a question that is asking you to think about what happens when you calculate an "average value" in order to lead you think about what the phrase "instantaneous velocity" could mean! You need to do it, not have someone else do it for you!
If at time t= 1.99 you are at point 2 and at time 2 you are position 2.01, you have moved from 2 to 2.01 so have moved a distance 2.01- 2= 0.01. And you did that in time interval 2- 1.99= 0.01.

If you move a distance 0.01 (km, say) in 0.01 (hours, say) what was your average velocity in that time interval?

Since velocity, in this way, is "the distance moved in a given time interval divided by the length of that time interval", do you see the problem with even defining "velocity at a given interval"?
 

Related to Advanced Functions Average vs. Instantaneous velocity

1. What is the difference between average velocity and instantaneous velocity?

Average velocity is the total displacement divided by the total time taken, while instantaneous velocity is the velocity at a specific moment in time. Essentially, average velocity gives an overall picture of an object's motion, while instantaneous velocity shows the velocity at a specific point in time.

2. How do you calculate average velocity?

To calculate average velocity, you divide the total displacement by the total time taken. This can be represented by the formula: average velocity = (final position - initial position) / (final time - initial time).

3. How is instantaneous velocity different from average velocity?

Instantaneous velocity is the velocity at a specific moment in time, while average velocity is the overall velocity over a certain period of time. Instantaneous velocity can change rapidly, while average velocity remains constant over the entire time interval.

4. Can average velocity be negative?

Yes, average velocity can be negative. This occurs when an object is moving in the opposite direction of its initial position. For example, if an object starts at position 10 and ends at position 5, its average velocity would be -5.

5. How is the concept of average velocity used in real-life scenarios?

The concept of average velocity is used in many real-life scenarios, such as calculating the average speed of a car during a road trip or determining the average velocity of a runner in a race. It is also used in physics and engineering to analyze the motion of objects and to make predictions about their future movements.

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