Answer:
Step-by-step explanation:
actually, it IS 7
Answer:
2, 3/4 and 1
Step-by-step explanation:
(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).)
1/2 x 2/3 x 3/4 = 1/4
(Sorry, I did the math wrong. I meant 1/4)