Answer
a. To left $2\lt t\lt 3$ and $5\lt t\lt 6$ sec.
To right $0\lt t\lt 1$ sec.
Still $ 1
Work Step by Step
a. Step 1. Given the $s(t)$ function, the velocity will be the derivative $v(t)=s'(t)$. $P$ will be moving to the left if the value of $v(t)$ is negative (indicated by a negative slope in the $s(t)$ curve): $2\lt t\lt 3$ and $5\lt t\lt 6$ sec.
Step 2. $P$ will be moving to the right if the value of $v(t)$ is positive (indicated by a positive slope in the $s(t)$ curve): $0\lt t\lt 1$ sec.
Step 3. P will be standing still if the value of $v(t)$ is zero (indicated by a zero slope in the $s(t)$ curve): $1\lt t\lt 2$ and $3\lt t\lt 5$ sec.
b. Velocity $v(t)$ will be the slopes of the line segments from the $s(t)$ function, and speed will be $|v(t)|$. Calculate the slopes for each time interval and graph the velocity and speed as shown in the figure.
