2. Two special unit vectors:
Unit vectors: dimensionless vectors of length 1
Two special unit vectors:
points in the +x direction
points in the +y direction

3. If you multiply a vector by a scalar, you multiply each of its components
That changes the length of the vector:

4. So we can represent vectors like this:

5. Adding and subtracting vectors:

6. Position vectors

7. Displacement vectors

8. Average velocity vectors

10. Instantaneous velocity vector
The instantaneous velocity is always tangent to the path

11. Average acceleration vectors

12. Instantaneous acceleration vector
Let the Dt become smaller and smaller, and the average acceleration becomes the instantaneous acceleration

13. When a has a component along the path, the speed is changing
Instantaneous acceleration vector
Let the Dt become smaller and smaller, and the average acceleration becomes the instantaneous acceleration
While the velocity vector is always tangent to the path, the acceleration generally is not.
When a has a component along the path, the speed is changing
When a has a component perpendicular to the path, the object is turning

14. Uniform Circular Motion
Constant speed motion in a circle
The acceleration is always pointed towards the center of the circle

15. An object moves along the brown path
An object moves along the brown path. Which vectors represent position, velocity, and acceleration? A)
A is position
C is velocity
B is acceleration B)
B is position
A is acceleration C)
C is position
B is velocity D)
A is position
B is velocity
C is acceleration E)
C is position
A is velocity
B is acceleration