A runner moves along a straight track according to the following sequence of one-dimensional displacements measured from the runner’s starting point:
+12 m, followed by –7 m, followed by +5 m.
Answer the questions below. Take the positive direction to be the forward direction along the track.
(a) Choose a convenient scale and draw three separate arrows that represent the individual displacements. Label each arrow with its algebraic value.
(b) On the same number line you created in part (a), construct a single arrow that graphically represents the resultant displacement of the runner. Clearly mark its starting and ending points.
(c) Determine the algebraic value of the resultant displacement by summing the three given displacements. Show your work.
(d) Compare the magnitude and direction of the resultant arrow from part (b) with the algebraic result from part (c). Explain any discrepancy that might appear between the two representations.