Question

when did the object have the greatest velocity? position (m) 0 --> 2 seconds 2 --> 3 seconds 3 --> 6 seconds 0 --> 6 seconds

Explanation:

Step1: Recall velocity - position graph relation

Velocity is the slope of the position - time graph.

Step2: Analyze slopes in different intervals

In the interval 0 - 2 seconds, the slope is $\frac{12 - 0}{2-0}=6$ m/s. In the interval 2 - 3 seconds, the slope is 0 m/s (constant position). In the interval 3 - 6 seconds, the slope is $\frac{2 - 12}{6 - 3}=\frac{- 10}{3}\approx - 3.33$ m/s.

Answer:

0 --> 2 seconds