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 $0$.