Question

find the following for path a in the figure below. (a) the distance traveled (in m) \boxed{} m (b) the magnitude of the displacement (in m) from start to finish \boxed{} m (c) the displacement (in m) from start to finish \boxed{} m

Explanation:

Part (a): Distance Traveled

Step1: Identify Path A's Movement

Path A starts at some point (let's assume start at \( x = 0 \) or left end) and moves right. From the graph, the horizontal axis (displacement \( x \) in m) shows that Path A moves from, say, \( x = 0 \) (or left) to \( x = 6 \) (since the arrow ends around \( x = 6 \), assuming start at \( x = 0 \) for simplicity? Wait, no, looking at the figure: Path A is a green arrow, B is blue left, C is red with a loop, D is orange with a loop. Wait, maybe Path A starts at \( x = 0 \) (green dot) and moves to \( x = 6 \) (since the arrow is horizontal to the right, ending at \( x = 6 \)? Wait, the x-axis has 0,2,4,6,8,10,12. Let's check: the green dot (A) is at left, arrow to right, so distance is the length of the path. So if it moves from, say, \( x = 0 \) to \( x = 6 \), distance is \( 6 - 0 = 6 \) m? Wait, maybe the start is at \( x = 0 \) (green dot) and end at \( x = 6 \), so distance traveled is the length of the path, which is the difference in x-coordinates. So distance \( d = 6 - 0 = 6 \) m? Wait, maybe the start is at \( x = 0 \) (green dot) and the arrow ends at \( x = 6 \), so distance is 6 m.

Step2: Calculate Distance

Distance is the total length of the path. For Path A, it's a straight line from start to end (no loops), so distance = end position - start position. If start at \( x = 0 \), end at \( x = 6 \), then distance \( = 6 - 0 = 6 \) m.

Step1: Define Displacement

Displacement is the straight-line distance from start to finish, regardless of path. Magnitude is the absolute value of displacement.

Step2: Calculate Displacement Magnitude

Start position: let's say \( x_i = 0 \) (green dot), end position \( x_f = 6 \) (end of green arrow). Displacement \( \Delta x = x_f - x_i = 6 - 0 = 6 \) m. Magnitude is \( |\Delta x| = 6 \) m.

Step1: Recall Displacement Formula

Displacement \( \Delta x = x_f - x_i \), where \( x_i \) is initial position, \( x_f \) is final position.

Step2: Substitute Values

Assume initial position \( x_i = 0 \) (start of Path A, green dot), final position \( x_f = 6 \) (end of green arrow). Then \( \Delta x = 6 - 0 = 6 \) m.

Answer:

(a):
\( \boldsymbol{6} \)

Part (b): Magnitude of Displacement