Average and Instantaneous Velocity

In summary, average velocity is the overall change in position over a specific period of time, while instantaneous velocity is the velocity at a particular moment in time. Average velocity is calculated by dividing the change in position (displacement) by the change in time. Yes, average velocity can be negative, indicating that the object is moving in the opposite direction of the positive direction. Instantaneous velocity is different from average velocity in that it represents the velocity at a single moment in time, while average velocity is an average of all velocities over a period of time. Calculating both average and instantaneous velocity allows us to understand how an object's velocity changes over time, with average velocity giving an overall picture and instantaneous velocity providing information about a specific moment in time.
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dmonlama
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Homework Statement


a. Show that if the position x of a moving point is given by a quadradic function of t,x = At^2 + Bt + C, then the average velocity over any time iunterval [t1,t2] is equal to the instantaneous velocity at the midpoint of the time interval.
b. What is the geometric significance of the result in part (a)?
 
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How do you calculate the average velocity over a given interval?
How do you calculate the instantaneous velocity at a given moment?
Can you give us the formulas?
 

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

Average velocity is the overall change in position over a specific period of time, while instantaneous velocity is the velocity at a particular moment in time.

2. How is average velocity calculated?

Average velocity is calculated by dividing the change in position (displacement) by the change in time.

3. Can average velocity be negative?

Yes, average velocity can be negative. This indicates that the object is moving in the opposite direction of the positive direction, or in other words, the displacement is negative.

4. How is instantaneous velocity different from average velocity?

Instantaneous velocity is the velocity at a single moment in time, while average velocity is the average of all velocities over a period of time. Instantaneous velocity can vary greatly from the average velocity if the object's speed is changing rapidly.

5. Why is it important to calculate both average and instantaneous velocity?

Calculating both average and instantaneous velocity allows us to understand how an object's velocity changes over time. Average velocity gives us an overall picture of the object's motion, while instantaneous velocity can tell us about the object's velocity at a specific moment in time.

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