Position-time graph illustrating an object's motion over 55 seconds, which serves as the basis for calculating velocity.

Okay, I see the final segment of the position-time graph. It's a straight line with a positive slope, indicating constant positive velocity. The line starts at t=40 seconds, x=-40 meters, and ends at t=60 seconds, x=0 meters. So, the velocity v = Δx / Δt = (0 m - (-40 m)) / (60 s - 40 s) = (40 m) / (20 s) = +2 m/s. This means from t=40 to t=60 seconds, the velocity is a constant +2 m/s. Now that I have calculated the velocity for all segments, I can summarize the results and describe the corresponding velocity-time graph.

Based on the analysis of the position-time (PT) graph, we can convert it into a velocity-time (VT) graph by calculating the slope (velocity) for each linear segment of the PT graph. Velocity is defined as the rate of change of position with respect to time, which is the slope of the position vs. time graph.

Here is the step-by-step solution:

1. Segment 1 (0 to 10 seconds):
* The object moves from position x = 0 m to x = 60 m.
* The change in position (Δx) is 60 m - 0 m = 60 m.
* The change in time (Δt) is 10 s - 0 s = 10 s.
* The velocity (v) is calculated as: v = Δx / Δt = 60 m / 10 s = +6 m/s.
* On the VT graph, this will be a horizontal line at +6 m/s from t=0 to t=10 s.

2. Segment 2 (10 to 15 seconds):
* The object's position remains constant at x = 60 m.
* Since there is no change in position (Δx = 0), the velocity is 0 m/s.
* On the VT graph, this will be a horizontal line at 0 m/s from t=10 to t=15 s.

3. Segment 3 (15 to 40 seconds):
* The object moves from position x = 60 m to x = -40 m.
* The change in position (Δx) is -40 m - 60 m = -100 m.
* The change in time (Δt) is 40 s - 15 s = 25 s.
* The velocity (v) is calculated as: v = Δx / Δt = -100 m / 25 s = -4 m/s.
* On the VT graph, this will be a horizontal line at -4 m/s from t=15 to t=40 s.

4. Segment 4 (40 to 60 seconds):
* The object moves from position x = -40 m to x = 0 m.
* The change in position (Δx) is 0 m - (-40 m) = +40 m.
* The change in time (Δt) is 60 s - 40 s = 20 s.
* The velocity (v) is calculated as: v = Δx / Δt = 40 m / 20 s = +2 m/s.
* On the VT graph, this will be a horizontal line at +2 m/s from t=40 to t=60 s.

Summary of the Velocity-Time Graph:

The resulting velocity-time graph will consist of four horizontal line segments:
* From t = 0 to 10 s: A line at v = +6 m/s.
* From t = 10 to 15 s: A line at v = 0 m/s.
* From t = 15 to 40 s: A line at v = -4 m/s.
* From t = 40 to 60 s: A line at v = +2 m/s.

This graph shows the constant velocity of the object during each distinct time interval.