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The graph shows the velocity of a cart over time, and you need to determine when the object is at rest. An object is at rest when its velocity is zero (v = 0 m/s).

From the graph, the velocity is zero at two specific time intervals:
1. Between **t = 5 s** and **t = 15 s**, the velocity is consistently at 0 m/s.
2. At **t = 20 s**, the velocity touches zero momentarily before increasing again.

Thus, the object is at rest during the following time intervals:
\[
t \in [5, 15] \cup \{20\} \, \text{seconds}.
\]

Would you like more details or have any further questions?

Here are some relative questions you might explore:
1. How can the object's position be determined from a velocity-time graph?
2. What is the significance of the slope in different parts of the velocity-time graph?
3. How would you calculate the total displacement of the object over time?
4. What does it mean if the velocity is negative on such a graph?
5. How can you calculate the object's acceleration from this graph?

**Tip**: When velocity remains constant over a period of time (flat line), the object is moving at a constant speed. If the velocity is zero during that time, the object is at rest.

Identify all times t when the object is at rest. You can use whatever math notation you are familiar with to indicate the set of time.

Learn how to identify when an object is at rest using a velocity-time graph. This problem explores key physics concepts such as velocity, time intervals, and kinematics, suitable for students in Grades 9-12.

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