2-3. Vectors, Scalars, and Coordinate Systems
What is the difference between distance and displacement? Whereas displacement is defined by both direction and magnitude, distance is defined only by magnitude. Displacement is an example of a vector quantity. Distance is an example of a scalar quantity. A
The direction of a vector in one-dimensional motion is given simply by a plus or minus sign. Vectors are represented graphically by arrows. An arrow used to represent a vector has a length proportional to the vector’s magnitude (e.g., the larger the magnitude, the longer the length of the vector) and points in the same direction as the vector.
Some physical quantities, like distance, either have no direction or none is specified. A
Coordinate Systems for One-Dimensional Motion
In order to describe the direction of a vector quantity, you must designate a coordinate system within the reference frame. For one-dimensional motion, this is a simple coordinate system consisting of a one-dimensional coordinate line. In general, when describing horizontal motion, motion to the right is usually considered positive, and motion to the left is considered negative. With vertical motion, motion up is usually positive and motion down is negative. In some cases, however, as with the jet in Figure 1, it can be more convenient to switch the positive and negative directions. For example, if you are analyzing the motion of falling objects, it can be useful to define downwards as the positive direction. If people in a race are running to the left, it is useful to define left as the positive direction. It does not matter as long as the system is clear and consistent. Once you assign a positive direction and start solving a problem, you cannot change it.
Check Your Understanding
A person’s speed can stay the same as he or she rounds a corner and changes direction. Given this information, is speed a scalar or a vector quantity? Explain.
Speed is a scalar quantity. It does not change at all with direction changes; therefore, it has magnitude only. If it were a vector quantity, it would change as direction changes (even if its magnitude remained constant).
A student writes, “A bird that is diving for prey has a speed of .” What is wrong with the student’s statement? What has the student actually described? Explain.
What is the speed of the bird in Exercise 1?
Acceleration is the change in velocity over time. Given this information, is acceleration a vector or a scalar quantity? Explain.
A weather forecast states that the temperature is predicted to be the following day. Is this temperature a vector or a scalar quantity? Explain.