Question

1. find the following for path a in figure 2.57: (a) the distance traveled. (b) the magnitude of the displacement from start to finish. (c) the displacement from start to finish.
2. find the following for path b in figure 2.57: (a) the distance traveled. (b) the magnitude of the displacement from start to finish. (c) the displacement from start to finish.
3. find the following for path c in figure 2.57: (a) the distance traveled. (b) the magnitude of the displacement from start to finish. (c) the displacement from start to finish.

Explanation:

Step1: Define distance and displacement concepts

Distance is total path - length, displacement is vector from start to finish.

Step2: Analyze path C

Let's assume start point of path C is at \(x = 4\) m and end - point is at \(x = 8\) m.

(a) Calculate distance traveled for path C

The object moves from \(x = 4\) m to \(x = 8\) m and then back to \(x = 4\) m.
Distance \(d=|8 - 4|+|8 - 4|=4 + 4=8\) m.

(b) Calculate magnitude of displacement for path C

The start and end points are the same (\(x = 4\) m). Magnitude of displacement \(|\Delta x|=|4 - 4| = 0\) m.

(c) Calculate displacement for path C

Displacement \(\Delta x=x_f-x_i\), where \(x_i = 4\) m and \(x_f = 4\) m. So, \(\Delta x=4 - 4=0\) m.

Answer:

(a) 8 m
(b) 0 m
(c) 0 m