Wrapping Function Homework: Avg. Velocity Calc

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In summary, the particle has a constant speed and moves in a circle with a radius of 5m in a counter-clockwise direction. It completes 1 revolution every 16 seconds. The average velocity for 1/4 revolution can be calculated using the equation (r2 - r1)/(t2 - t1), where r represents position and t represents time. For 1/4 revolution, the time interval would be 4 seconds and the position interval would be 5m. Therefore, the average velocity for 1/4 revolution would be 5m/4s. For 5/4 revolutions, the time interval would be 20 seconds and the position interval would be 25m. Therefore, the average
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Homework Statement



A particle moves with constant speed in a circle with a radius of 5m in a counter-clockwise direction. It makes 1 revolution every 16 seconds.

What is the average velocity for 1/4 revolution? 5/4 revolutions?

Homework Equations



Wrapping Function: W = (cos t, sin t)

Avg. Velocity = (r2 - r1)/(t2 - t1)
where r represents position and t represents time.

The Attempt at a Solution



I don't really have an attempt. I can't figure out how to import the 5m radius and 16 second revolution part into the equation.
 
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I know the equation for average velocity is (r2 - r1)/(t2 - t1). But how do I use that when it's just one circle?
 

FAQ: Wrapping Function Homework: Avg. Velocity Calc

What is a wrapping function?

A wrapping function is a mathematical concept that allows for the calculation of average velocity. It involves breaking down a complex motion into smaller intervals and calculating the average velocity for each interval, then taking the average of all the intervals to find the overall average velocity.

How is average velocity calculated using a wrapping function?

To calculate average velocity using a wrapping function, you first need to determine the time intervals for which you want to calculate the average velocity. Then, you need to calculate the total displacement for each interval. Finally, divide the total displacement by the total time to find the average velocity for each interval. The overall average velocity is then calculated by taking the average of all the interval velocities.

What is the purpose of using a wrapping function to calculate average velocity?

The purpose of using a wrapping function is to accurately calculate the average velocity of a complex motion, where the velocity may change at different points in time. By breaking down the motion into smaller intervals and calculating the average velocity for each interval, we can get a more precise measurement of the overall average velocity.

Can a wrapping function be used for any type of motion?

Yes, a wrapping function can be used for any type of motion, as long as the time intervals are chosen appropriately. However, it is most commonly used for motions where the velocity changes at different points in time, such as in circular or oscillatory motion.

Are there any limitations to using a wrapping function for calculating average velocity?

One limitation of using a wrapping function is that it assumes the velocity remains constant within each time interval. This may not always be the case for complex motions, leading to some error in the calculated average velocity. Additionally, the choice of time intervals can also affect the accuracy of the calculation. It is important to choose appropriate time intervals that accurately capture the changes in velocity for the motion being analyzed.

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