Final answer:
The object changed its velocity over a period of 2 seconds, from the time it started accelerating at t = 2 seconds to when it reached a constant velocity at t = 4 seconds. So, the correct answer is Option 1: 4 seconds.
Step-by-step explanation:
To determine how much time it took for the object to change its velocity, we need to study the description of the object's motion and the given velocity values.
Initially, the object is at rest and starts accelerating at t = 2 s, continues this acceleration for 2 seconds until t = 4 s, and then travels at a constant velocity from t = 4 s to t = 6 s.
As the velocity vs. time graph shows a constant gradient from t = 4 s to t = 6 s, we can infer that no change in velocity occurred after t = 4 s until t = 6 s.
Therefore, the total change in velocity takes place from the moment the object starts to accelerate at t = 2 s until it reaches a constant velocity at t = 4 s, which is a duration of 2 seconds.
Thus, the correct answer is Option 1: 4 seconds.