Question

1. no calculator a bug begins to crawl up a vertical wire at time t = 0. the velocity v of the bug at time t, 0 ≤ t ≤ 8, is given by the function whose graph is shown above. at what value of t does the bug change direction? (a) 2 (b) 4 (c) 6 (d) 7 (e) 8

Explanation:

Step1: Understand velocity - direction relation

A bug changes direction when its velocity changes sign (from positive to negative or negative to positive). Positive velocity means moving up, negative means moving down.

Step2: Analyze velocity graph

• From \(t = 0\) to \(t = 6\), velocity \(v\) is non - negative (above or on the \(t\) - axis), so the bug is moving up (or at rest, but here velocity is positive or zero in a non - decreasing then constant then non - increasing way).
• At \(t = 6\), the velocity \(v = 0\), and for \(t>6\) (like \(t = 7,8\)), the velocity is negative (below the \(t\) - axis), meaning the bug starts moving down. So the bug changes direction at \(t = 6\) as the velocity changes from non - negative to negative.

Answer:

C. 6