A particle moves along a straight line. The graph of the particle's velocity \(v(t)\) at time \(t\) is shown above for \(0\leq t \leq m\), where \(j\), \(k\), \(l\), and \(m\) are constants. The graph intersects the horizontal axis at \(t=0\), \(t=k\), and \(t=m\) and has horizontal tangents at \(t=j\) and \(t=l\). For what value of \(t\) is the speed of the particle decreasing?

Summary Submit

Speed reflects the magnitude of the velocity. Speed decreases as long as \(|v(t)|\) decreases.

From the graph, we can see that speed decreases from \(j\) to \(k\).

It may be tempting to say that the speed continues to decrease from \(k\) to \(l\), but in fact, speed increases here.

To use a real-world example, if you start reversing your car faster, you are still technically going faster and your speed goes up.

From \(l\) to \(m\), you are "reversing" slower and your speed is decreasing until you hit a speed of \(0\).