Question

a particle moves along the x - axis. the graph of the particles velocity v(t) at time t is shown above for 0 < t < 4.5. how many times does the particle change direction over the time interval 0 < t < 4.5?
a) two
b) three
c) five
d) seven

Explanation:

Step1: Recall velocity - direction relationship

A particle changes direction when its velocity changes sign (from positive to negative or vice - versa).

Step2: Analyze the graph

We look at the graph of \(v(t)\) for \(0 < t<4.5\). The velocity function \(v(t)\) crosses the \(t\) - axis (where \(v(t)=0\)) three times in the interval \(0 < t < 4.5\). Each time \(v(t)\) crosses the \(t\) - axis, the sign of \(v(t)\) changes, which means the particle changes direction.

Answer:

B. Three