A whole new class of problems raises its ugly head when we consider two simultaneous motions of a particle. We have had some contact with this already, but it is most graphically illustrated by problems of boats traveling across streams. Before we launch into this, however, we need to return for a moment to the contemplation of vectors . In physics a vector is any quantity described by both a magnitude and a direction, while a scalar needs only magnitude. Thus quantities like velocity, displacement, electric field, and momentum are vectors, quantities like pressure, speed, energy, and time are scalars.
Vectors add in a peculiar but logical way.
Travel straight for 3.0 miles, make a turn to the left, and walk for 4 more miles. We will deal almost exclusively with vectors that are at right angles to each other, but it is not difficult to see how more general addition can be accomplished. Just end up with little parallelograms instead of little rectangles. To subtract vectors, simply add the negative of the subtracted vector. Note the direction and magnitude of each of the vectors A , B , C , and D .