A particle whose velocity is given by a graph

The question

Name: ______________________   Date: ____________   A particle whose velocity is given by a graph (9 points)

1. (a) A particle moves along the $x$-axis with velocity $v(t)$ shown in the graph, for $0 \le t \le 12$ seconds. Find the acceleration of the particle at $t = 5$. Is the particle speeding up or slowing down at $t = 5$? Give a reason for your answer. [2 points]

2. (b) At what times $t$ in $0 < t < 12$ does the particle change direction? Justify your answer. [2 points]

3. (c) The particle is at $x = 5$ at time $t = 0$. Find its position at $t = 12$. [2 points]

4. (d) Find the total distance the particle travels over $0 \le t \le 12$. At what time is the particle farthest to the left? Justify your answer. [3 points]