At time $t = 0$, two points P and Q simultaneously depart from the origin and move on a number line. Their velocities at time $t$ ($t \geq 0$) are respectively $$v_1(t) = t^2 - 6t + 5, \quad v_2(t) = 2t - 7$$ Let $f(t)$ denote the distance between points P and Q at time $t$. The function $f(t)$ increases on the interval $[0, a]$, decreases on the interval $[a, b]$, and increases on the interval $[b, \infty)$. Find the distance traveled by point Q from time $t = a$ to time $t = b$. (Here, $0 < a < b$) [4 points] (1) $\frac{15}{2}$ (2) $\frac{17}{2}$ (3) $\frac{19}{2}$ (4) $\frac{21}{2}$ (5) $\frac{23}{2}$
At time $t = 0$, two points P and Q simultaneously depart from the origin and move on a number line. Their velocities at time $t$ ($t \geq 0$) are respectively
$$v_1(t) = t^2 - 6t + 5, \quad v_2(t) = 2t - 7$$
Let $f(t)$ denote the distance between points P and Q at time $t$. The function $f(t)$ increases on the interval $[0, a]$, decreases on the interval $[a, b]$, and increases on the interval $[b, \infty)$. Find the distance traveled by point Q from time $t = a$ to time $t = b$. (Here, $0 < a < b$) [4 points]\\
(1) $\frac{15}{2}$\\
(2) $\frac{17}{2}$\\
(3) $\frac{19}{2}$\\
(4) $\frac{21}{2}$\\
(5) $\frac{23}{2}$