Question 1

In the sequence of images above, a person is shown at two different positions in front of a garage. If the leftmost position is taken as the origin ($$x = 0$$), and the distance between the two positions is $$3.0$$ meters to the right, what is the displacement vector of the person from the first to the second position?

Accepted Answer

$$\Delta \vec{r} = +3.0\ \mathrm{m}\ \hat{\imath}$$

Question 2

Suppose the person in the images walks from the leftmost position to the rightmost position, then turns around and walks back to the starting point. What is the total distance traveled and the net displacement?

Accepted Answer

Distance traveled: $$6.0\ \mathrm{m}$$, Displacement: $$0\ \mathrm{m}$$

Question 3

If the person takes $$4.0$$ seconds to walk from the leftmost position to the rightmost position, what is their average velocity during this interval?

Accepted Answer

$$\vec{v}_{\mathrm{avg}} = \dfrac{+3.0\ \mathrm{m}}{4.0\ \mathrm{s}} = +0.75\ \mathrm{m/s}\ \hat{\imath}$$

Question 4

If the person pauses at the rightmost position for $$2.0$$ seconds before returning to the leftmost position in another $$4.0$$ seconds, what is their average speed for the entire trip?

Accepted Answer

Average speed $$= \dfrac{6.0\ \mathrm{m}}{10.0\ \mathrm{s}} = 0.60\ \mathrm{m/s}$$

Question 5

Which of the following statements best describes the difference between distance and displacement as illustrated by the images?

Accepted Answer

Distance is the total length of the path traveled, while displacement is the straight-line vector from the initial to the final position.

Question 6

If the person starts at the leftmost position, walks to the rightmost position, and then stands still for $$5$$ seconds, what is their velocity during the time they are standing still?

Accepted Answer

$$0\ \mathrm{m/s}$$

Question 7

If the positive $$x-$$axis is defined to the right, and the person moves from $$x = 2.0\ \mathrm{m} to$$ $$x = -1.0\ \mathrm{m}$$, what is the $$x$$ component of their displacement?

Accepted Answer

$$\Delta x = -1.0\ \mathrm{m} - 2.0\ \mathrm{m} = -3.0\ \mathrm{m}$$

Question 8

Which of the following best describes the type of quantity represented by displacement?

Accepted Answer

A vector, because it has both magnitude and direction.

Question 9

If the person in the images walks from the leftmost position to the rightmost position in $$3.0$$ seconds, what is the slope of the position vs. time graph for this interval?

Accepted Answer

Slope $$= \dfrac{3.0\ \mathrm{m}}{3.0\ \mathrm{s}} = 1.0\ \mathrm{m/s}$$

Question 10

If the person reverses direction and walks back to the starting point in the same amount of time, what is their average velocity for the entire round trip?

Accepted Answer

Average velocity $$= 0\ \mathrm{m/s}$$

Motion in One Dimension: Position, Displacement, and Vectors

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