Vectors and Scalars

When we considered 1-dimensional motion we only had two directions to worry about, namely motion to the Right or motion to the Left and we indicated direction with a + or - sign. We found that the following quantities had a direction (i.e. could take a + or - sign): displacement, velocity and acceleration. Quantities that don't have a sign were distance, speed and magnitude of acceleration. Now in 2 and 3 dimensions we need more than a + or - sign. That's where vectors come in. Vectors are quantities with both magnitude and direction. Scalars are quantities with magnitude only. Examples of Vectors are: displacement, velocity, acceleration, force, momentum, electric field Examples of Scalars are: distance, speed, magnitude of acceleration, time, temperature Before delving into vectors consider the following problem.

Example Joe and Mary are rowing a boat across a river which is 40 m wide. They row in a direction perpendicular to the bank. However the river is °owing downstream and by the time they reach the other side, they end up 30 m downstream from their starting point. Over what total distance did the boat travel?

Solution Obviously the way to do this is with the triangle in Fig. 1.1, and we deduce that the distance is 50 m.

FIGURE 1.1 Graphical solution to river problem.