# Distance & Displacement

- Author:
- Matt Dyck

This applet shows object B starting at the the reference point A at (10 , 0) and moving in a half circle as the time increases. Both the distance travelled on the circle and the displacement vector are shown. The x (West) and y (North) components of the displacement vector are also shown.
The only control is the time slider which you can control with the pointer tool at the top left.

1. The circumference of a circle is found using using the equation . The radius of our circle is 10. What would be the distance around a whole circle with a radius of 10?

2. We only have half a circle, so if object B was to move from the start to position 4 what should be the distance travelled around the circle? Check your answer by moving the slider all the way to the right, making object B move to Position 4.

3. Reset. (button at the top right)

4. Move the slider so that object B ends up at Position 4. As you do so, does the distance travelled ever have the same value of the displacements magnitude? Does it ever become less, equal to or more?

5. Reset.

6. Move the slider so that the vector is at Position 1. Is the value of the distance travelled larger or smaller than the magnitude of the displacement?

7. At Position 1, note that the displacement and it's west and north components form a right angle triangle. That means that the we can find the magnitude of the displacement by finding the hypotenuse of the triangle.
a. Use to confirm this.
b. Which trigonometry ratio could we use to find the angle in this triangle? Use that ratio to confirm that the angle is 63.44 .

8. Without moving the slider
a. determine how far object B will have travelled to get to Position 2. (Hint: It's the way around a circle with a radius of 10. ).
b. determine how far object B will travel to the west and north.
c. determine the magnitude and direction of object B's displacement using your answer from 4b. Once you've done that, move the slider to Position 2 to check your answer.

9. Without moving the slider, determine what the displacement of object B at Position 3 would be. Include the magnitude and direction. Once you've done that, move the slider to Position 3 to check your answer.