Single Variable Calculus, Chapter 3, 3.7, Section 3.7, Problem 5

Below are the graphs of the velocity functions of two particles, where $t$ is measured in seconds. At what time each particle speeding up? Slowing down? Explain.

a.)








The particle is speeding up when the velocity is increasing (either in the positive or negative direction). On the other hand the particle is slowing down when the velocity is decreasing.

Based from the graph we can say that the particle is speeding up on intervals $0 \leq t \leq 1$ and $2 \leq t \leq 3$ (speeding up on the negative direction). While the particle is slowing down on interval $1 < t < 2$.

b.)







Based from the graph, we can say that the particle is speeding up at intervals $1 < t < 2$ and $3 < t \leq 4 $ (in the negative direction). While it slows down at intervals $0 \leq t \leq 1$ and $2 \leq t \leq 3$.

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