12. (2011, AB-1) (Calculator Permitted) For 0
t , a particle is moving along the x-axis. The particle’s
6
t
/4
x t , is not explicitly given. The velocity of the particle is given by
v t
e
position,
2sin
. The
1
1
t
t
/4
/4
x
acceleration of the particle is given by
a t
e
cos
e
and
0
.
2
2
(a) Is the speed of the particle increasing or decreasing at time
t
5.5
? Give a reason for your answer.
(b) Find the average velocity of the particle for the time period 0
t .
6
(c) Find the total distance traveled by the particle from time
t
to
t .
0
6
t , the particle changes direction exactly once. Find the position of the particle at that time.
(d) For 0
6