(d) The particle moves in the positive direction when its velocity has a positive sign. You know the particle is at rest when
and
, and because the velocity function is continuous, you need only check the sign of
for values on the intervals (0, 3) and (3, 6).
We have, for instance
and
, which means the particle is moving the positive direction for
, or the interval (3, 6).
(e) The total distance traveled is obtained by integrating the absolute value of the velocity function over the given interval:

which follows from the definition of absolute value. In particular, if
is negative, then
.
The total distance traveled is then 4 ft.
(g) Acceleration is the rate of change of velocity, so
is the derivative of
:

Compute the acceleration at
seconds:

(In case you need to know, for part (i), the particle is speeding up when the acceleration is positive. So this is done the same way as part (d).)
Answer:
Step-by-step explanation:
11x-3+5x-9=180
16x-12=180
16x=192
x=12
<pst=129
Answer:
36-2n<1/3n+15
Step-by-step explanation:
There are multiple solutions. One solution is 30. Because 30 times 2 is 60 and 36-60 is less than 1/3 of 30 (10) plus 15.