Question

Suppose that the graph of the velocity function of a particle is as shown in the figure, where t is measured in seconds. When is the particle traveling forward (in the positive direction)? When is it traveling backward? What is happening when \(5 < t < 7\)?

Short answer

The particle traveling in the forward direction for \(7 < t < 8\), traveling backward for \(7 < t < 8\), and for \(5 < t < 7\), the particle is at rest.

Step-by-step solution

Analyze the duration of positive velocity

The positive velocity means that the particle is moving in the forward direction. From the graph given, this duration is \(0 < t < 5\) .

Analyze the duration of positive velocity

The negative velocity means that the particle is moving in the backward direction. From the graph given, this duration is \(7 < t < 8\) .

Analyze the duration of zero velocity

The zero-velocity means that the particle is not moving and is at rest. From the graph given, this duration is \(5 < t < 7\) .