Question

an object moves in a straight line. the graph below is the objects velocity at time t. for which values of t between 0 and 14 is the object moving forward? use interval notation. if applicable, separate multiple intervals with the \∪\ operator.

Explanation:

Step1: Identify forward motion condition

An object moves forward when its velocity \(v(t) > 0\).

Step2: Find intervals with \(v(t) > 0\)

Look at the velocity graph:

• From \(t=5\) to \(t=9\), \(v(t) > 0\)
• From \(t=9\) to \(t=14\), \(v(t) > 0\) (excluding \(t=9\) where \(v(t)=0\), and including up to \(t=14\) where \(v(t)=0\))

Answer:

\((5, 9) \cup (9, 14)\)