Calculating Displacement and Average Velocity/Acceleration for Circular Motion

[nwells1998]

What is the difference between average acceleration and average velocity?

 

[Doc Al]

Velocity and acceleration are two different quantities. Velocity is the rate of change of displacement; acceleration is the rate of change of velocity.

 

[nwells1998]

So can an object have the same average velocity and average acceleration?

 

[Dale]

So can an object have the same average velocity and average acceleration?

No, the units are different. You might have an object with an average velocity of 1 m/s and an average acceleration of 1 m/s², but those are not the same despite both having the number 1. Just like 1 orange is not the same as 1 apple.

 

[nwells1998]

An athlete starts at point A and runs at a constant speed of 6.0m/s around a round track 100m in diameter. find the x and y components of this runners average velocity and acceleration between points a, b, c, d (equally apart on circle).

So there is no acceleration because the speed is constant?

 

[Dale]

An athlete starts at point A and runs at a constant speed of 6.0m/s around a round track 100m in diameter. find the x and y components of this runners average velocity and acceleration between points a, b, c, d (equally apart on circle).

So there is no acceleration because the speed is constant?

Both velocity and acceleration are vector quantities. In other words they have a magnitude and a direction. If you change the direction of your velocity you have accelerated even if you have not changed the magnitude of your velocity (speed).

 

[nwells1998]

ah...okay I see...thanks, i will start working on this problem!

 

[nwells1998]

So...tell can you please tell me if I am on the right track?

A = (-50, 0) B = (0,50) C = (50, 0) D = (0, -50)

Circumference = (pi * r^2) = 7854m

time between points = 7854m / 6.0m/s = 1309 s

X components:
Vax, A = (0-50m)/1309s = -0.038 m/s

Aax, A = (0-50m/s)/1309s = -.038m/s/s

 

[Doc Al]

So...tell can you please tell me if I am on the right track?

A = (-50, 0) B = (0,50) C = (50, 0) D = (0, -50)

Circumference = (pi * r^2) = 7854m

Careful: You found the area instead of the circumference.

time between points = 7854m / 6.0m/s = 1309 s

Correct this. Also: The points are spaced 1/4 circumference apart.

To find the average velocity between points A and B, for example, first find the displacement between A and B. (It's a vector that points from A to B.)

 

[nwells1998]

oops...okay so the circumference is 314m.

Time between points is 314m / 6.0m/s / 4 13.0s between each section.

so for A - b

displacement Ax = (0-50m)/13s = -3.84 m/s
displacement Ay, A = (50-0)/13s = 3.84 m/s

VA = sq rt[(-3.84^2)+(3.84^2)] = 5.43 m/s

Aax = 3.84m/s^2 Aay = -3.84m/s^2

 

[alphysicist]

Hi nwells1998,

oops...okay so the circumference is 314m.

Time between points is 314m / 6.0m/s / 4 13.0s between each section.

so for A - b

displacement Ax = (0-50m)/13s = -3.84 m/s
displacement Ay, A = (50-0)/13s = 3.84 m/s

I don't believe this is right for the displacement, even though some of your numbers are right. Let's say point A is 50m to the west of the circle and point B is 50 m to the north of the circle. To find the displacement, you need to know how far B is from A, and also what direction B is from A. What would those answers be?

Then the average velocity is found from:

average velocity = displacement / time

VA = sq rt[(-3.84^2)+(3.84^2)] = 5.43 m/s

Aax = 3.84m/s^2 Aay = -3.84m/s^2

The average acceleration is (change in velocity)/(change in time). To answer that, you need to know what the velocities are at A and B. What are those?