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

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

So we can represent vectors like this:

Adding and subtracting vectors:

Position vectors

Displacement vectors

Average velocity vectors

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

Average acceleration vectors

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

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

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

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