# Vectors in context

A moving object that has an initial position vector of and is moving at a constant velocity of , has the following position vector at time t:

A moving object that has an initial velocity vector of and is moving with a constant acceleration of , has the following velocity vector at time t:

Speed is found by taking the magnitude of the velocity vector.

** Example 1** – *Find the position vector, at time t = 3 minutes, of a plane that starts at position vector and moves at a constant velocity of kilometres per minute where i and j are unit vectors in the x and y directions respectively.*

Using the first formula above with and as given and t=3 gives .

**Example 2** – *A 12:00am, a ship has position vector where i and j are unit vectors in the x and y directions respectively. At 3:00pm, the ship has position vector . Find the speed of the ship.*

The ship moves by in three hours. This means that the shipping is moving every hour. This is a velocity vector and the corresponding speed is found from the magnitude of this vector:

Speed = units per hour.