Question
Physics 211 - Please refer back to the June 13, 1997 Question, in particular the definitions of displacement and distance travelled, and to the June 20, 1997 Question, which has examples of graphs. These questions are available in the Question Archive. (Analytical Geometry. Graphs.)
Suppose a hiker leaves his camp at time t = 0 in the morning and returns to his camp two hours later. Various hypothetical graphs of distance travelled, s, vs. time elapsed, t, for the hike are shown above.
Which graph (or graphs) could represent the distance travelled by the hiker vs. time elapsed? Give reasons, both for the possible and the impossible graphs.
Answer
Graph (c) is the only one that could represent the distance travelled by the hiker vs. the time elapsed. The four graphs will now be discussed in alphabetical sequence.
Graph (a). Graph (a) is two-valued, i.e., for a given t, it gives two values of s. This is impossible. When a certain amount of time t has elapsed, only one distance s can have been travelled.
Graph (b). Graph (b) shows an s that is non-zero at the start of the motion at t = 0. That is impossible. At the start of the motion, the distance travelled since the start must be zero.
Also, graph (b) shows s to be decreasing at first. That is impossible. The distance travelled is an additive quantity that can never decrease. It can remain constant, when the travelling object is at rest, or it can increase, when the travelling object is moving.
Graph (c). This graph is possible: s starts at s = 0 at the start of the motion at t = 0, and s is increasing all the time. At any given time, s has a unique value.
Graph (d). This graph is impossible because s is decreasing in the right half of the graph. See the second paragraph of the discussion of graph (b).