By Ivan, V. Meshchersky, N.M. Sinelnikova

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D. A quantity that remains constant over time. e. A quantity that decreases faster and faster over time. f. A quantity that decreases slower and slower over time. g. A quantity that decreases at a steady rate over time. 3. For each of the following situations (familiar from Chapter 1), sketch a non-numerical graph of the given quantity as a function of time. Then, immediately below that, make a graph of the rate of change of the quantity as a function of time. Align the graphs carefully. a. It’s 80◦ F in your kitchen.

In general, objects move in curved paths at varying speeds. Just think of a ﬂy buzzing around a bowl of peaches. See Figure 35. The Position Vector in Curvilinear Motion Figure 36 shows the position vector r of the buzzing ﬂy at three instants of time. Because the ﬂy is moving, the position vector will Chapter 3 Introducing Position and Velocity 39 FIGURE 35. A ﬂy buzzing around a bowl of peaches. Its path is curved, and its speed also varies over time. r(t3) r(t1) r(t2) origin depend on time, as r(t).

For example, we might call the treasure’s position vector r. Arrow symbols like this are usually used in handwriting. In typed or printed documents like this book, vectors are usually named using boldface letters. So in this book we’ll use a symbol like r to represent the position of the treasure. Position versus Distance Position is not the same as our everyday term distance. Distance refers only to “how far” away something is from the origin. But the position of an object refers both to how far away it is from the origin and to its direction from the origin.