Question

which graph best represents the relationship between \velocity\ and \time\ for an object that is slowing down for 2 seconds, then moves at a constant velocity for 1 second, and finally speeds up for 3 seconds?

Explanation:

Step1: Analyze slowing - down phase

When an object is slowing down, the velocity - time graph has a negative slope. This occurs from \(t = 0\) to \(t=2\) seconds.

Step2: Analyze constant - velocity phase

When an object moves at a constant velocity, the velocity - time graph is a horizontal line. This occurs from \(t = 2\) to \(t = 3\) seconds.

Step3: Analyze speeding - up phase

When an object is speeding up, the velocity - time graph has a positive slope. This occurs from \(t=3\) to \(t = 6\) seconds.

Answer:

The second graph (from the top) best represents the motion as it has a negative - slope segment from \(t = 0\) to \(t = 2\) seconds, a horizontal segment from \(t = 2\) to \(t=3\) seconds, and a positive - slope segment from \(t = 3\) to \(t = 6\) seconds.