A particle with velocity 4cos(0.9t) - 0.2t

Name: ______________________ Date: ____________ A particle with velocity 4cos(0.9t) - 0.2t (9 points)

Table

The velocity of a particle, in meters per second, for 0 ≤ t ≤ 6 seconds, and its position at t = 0
Quantity	Value
$v(t)$	$4\cos(0.9t) - 0.2t$ meters per second, $0 \le t \le 6$
$x(0)$	3 meters

(a) Is the speed of the particle increasing or decreasing at time $t = 2$ ? Give a reason for your answer. [2 points]
(b) Find all times $t$ in $0 < t < 6$ at which the particle changes direction. Justify your answer. [2 points]
(c) Find the position of the particle at time $t = 6$ . [2 points]
(d) Find the total distance traveled by the particle over $0 \le t \le 6$ . Find the average velocity of the particle over the same interval. Indicate units of measure. [3 points]

The question