Scalars vs. Vectors

Scalars- measurements that have no direction to them Examples: Distance, speed

Vectors- measurements that have a direction to them Examples: displacement, velocity

Displacement vs. Distance

Displacement - the most direct route from one point to another. (The net distance traveled)

Distance- the length traveled

Example Problem:

If a car travels 3m directly east then 5m directly west, what is the displacement and what is the distance traveled?

Displacement: if a car goes 3m east, and then it goes 5m opposite of east, the car will travel enough to cancel out the 3m east traveled, and go an extra 2m after that. This is best represented in an equation:

If east is positive:

=3m (east) + 5m (opp. east)

=3m (east) + (-5)m east

= -2m east

= 2m west

Displacement is often represented by the variable s, or x.

Velocity vs. Speed

Speed- change in distance over change in time

Velocity- the change in displacement divided by the change in time. It is also defined as the derivative of the displacement equation. Velocity is a vector.