HI PLEASE HELP ME WITH MY CALCULUS 1 HW? I AM REALLY STUCK. I need help with parts d, e,g.

(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).)