A particle moves along the $x$-axis so that its velocity $v$ at time $t$, for $0 \leq t \leq 5$, is given by $v(t) = \ln\left(t^2 - 3t + 3\right)$. The particle is at position $x = 8$ at time $t = 0$. (a) Find the acceleration of the particle at time $t = 4$. (b) Find all times $t$ in the open interval $0 < t < 5$ at which the particle changes direction. During which time intervals, for $0 \leq t \leq 5$, does the particle travel to the left? (c) Find the position of the particle at time $t = 2$. (d) Find the average speed of the particle over the interval $0 \leq t \leq 2$.
A particle moves along the $x$-axis so that its velocity $v$ at time $t$, for $0 \leq t \leq 5$, is given by $v(t) = \ln\left(t^2 - 3t + 3\right)$. The particle is at position $x = 8$ at time $t = 0$.
(a) Find the acceleration of the particle at time $t = 4$.
(b) Find all times $t$ in the open interval $0 < t < 5$ at which the particle changes direction. During which time intervals, for $0 \leq t \leq 5$, does the particle travel to the left?
(c) Find the position of the particle at time $t = 2$.
(d) Find the average speed of the particle over the interval $0 \leq t \leq 2$.