Question

what is the distance traveled by the object between 1 and 3 seconds as seen in this graph? m
what is the total distance traveled by the object as seen in this graph? m
what is the total displacement of the object as seen in this graph? m

Explanation:

Step1: Find distance from 1 - 3 seconds

The object is at a constant position of $y = 3$ m from $t = 1$ s to $t=3$ s. So the distance traveled is $0$ m.

Step2: Calculate total distance

From $t = 0$ to $t = 3$ s, position is constant at $y = 3$ m (distance $d_1=0$ m). From $t = 3$ s to $t = 5$ s, it moves from $y = 3$ m to $y = 2$ m, $d_2=\vert3 - 2\vert= 1$ m. From $t = 5$ s to $t = 6$ s, it moves from $y = 2$ m to $y = 1$ m, $d_3=\vert2 - 1\vert = 1$ m. From $t = 6$ s to $t = 7$ s, it moves from $y = 1$ m to $y=-2$ m, $d_4=\vert1-(-2)\vert=3$ m. Total distance $d=d_1 + d_2+d_3 + d_4=0 + 1+1 + 3=5$ m.

Step3: Calculate total displacement

Initial position at $t = 0$ is $y = 3$ m and final position at $t = 7$ s is $y=-2$ m. Displacement $\Delta y=-2 - 3=-5$ m, and magnitude of displacement is $5$ m.

Answer:

0
5
5