Answer
a. $t=2$ sec and $t=7$ sec,
b. $3\leq t\leq 6$ sec,
c. See graph.
d. See graph.
Work Step by Step
a. The body reverses direction whenever its velocity changes sign (+ to - or - to +) and we can identify that at $t=2$ sec and $t=7$ sec, the velocity switched signs, which means that it reversed directions.
b. The body will be moving at a constant speed when the slope of the velocity curve is zero. We can identify that during $3\leq t\leq 6$ sec, the speed did not change.
c. The body’s speed is $|v(t)|$, so we need to reverse all the negative regions to positive from the original velocity curve as can be seen from the graph.
d. The acceleration is the derivative of the velocity. We can calculate the slope values of each line segment and graph the acceleration as shown in the figure.
