Question

what is the total distance traveled by the object as seen in this graph?
what is the total displacement of the object as seen in this graph?

Explanation:

Step1: Analyze first - stage motion

From \(t = 0\) s to \(t = 1\) s, the object moves from \(x = 0\) m to \(x = 3\) m. The distance \(d_1=3 - 0=3\) m.

Step2: Analyze second - stage motion

From \(t = 1\) s to \(t = 3\) s, the object is at rest, so the distance \(d_2 = 0\) m.

Step3: Analyze third - stage motion

From \(t = 3\) s to \(t = 4\) s, the object moves from \(x = 3\) m to \(x = 4\) m. The distance \(d_3=4 - 3 = 1\) m.

Step4: Analyze fourth - stage motion

From \(t = 4\) s to \(t = 6\) s, the object moves from \(x = 4\) m to \(x = 0\) m. The distance \(d_4=4 - 0=4\) m.

Step5: Calculate total distance

The total distance \(d=d_1 + d_2+d_3 + d_4=3+0 + 1+4=8\) m.

Step6: Calculate displacement

The initial position \(x_i = 0\) m and the final position \(x_f=0\) m. Displacement \(\Delta x=x_f - x_i=0 - 0 = 0\) m.

Answer:

Total distance: 8
Total displacement: 0