Question

g) the velocity of a particle is given in the graph above for 0 ≤ t ≤ 11. how many times on the interval does the particle change directions?

Explanation:

Step1: Understand the relationship between velocity and direction

When the velocity \(v(t)\) of a particle changes sign (from positive to negative or vice - versa), the particle changes its direction of motion.

Step2: Analyze the graph for sign changes

Looking at the velocity - time graph (\(v(t)\) vs \(t\)):

• A sign change of \(v(t)\) implies a direction change.
• From the graph, we can observe that the velocity function \(v(t)\) crosses the \(t\) - axis (where \(v(t)=0\)) at two distinct points in the interval \(0\leq t\leq11\).

Answer:

The particle changes direction \(2\) times.