.
The position function of a moving object is .
a. When t = 2, what is the position of the object?
b. Determine the velocity function v(t).
c. For what valid values of t has the object stopped?
d. Determine the intervals when the object is moving east and moving west for valid values of t.
e. Is the object moving away or toward the origin at t = 2 s?
f. What is the acceleration function a(t)?
g. At t = 2 is the object speeding up or slowing down?
h. Determine the total distance travelled in the first 5 seconds.
~~~~~~~~~~~~~~~
(a) It is s(2). Substitute t= 2 into the formula and calculate.
I will not calculate it for you. It is YOUR job.
(b) To get the velocity function v(t), differentiate the given position function over t.
I will not differentiate it for you - it is YOUR job.
(c) These values of t are those where the velocity function is zero.
In other words, you need to solve the equation v(t) = s'(t) = 0.
This equation is formally of the third degree, but it can be factored and reduced to the lower degrees equations.
(d) The object is moving east if (and where) v(t) > 0.
The object is moving west if (and where) v(t) < 0.
(e) Calculate s(2) and v(2).
If s(2) < 0 and v(2) > 0, the object moves toward the origin.
If s(2) > 0 and v(2) < 0, the object moves toward the origin.
Otherwize, it moves away from the origin.
(f) Acceleration a(t) is the SECOND derivative of the position function over t.
(g) If v(2) > 0 and a(2) > 0, then the object is speeding (in the East direction).
If v(2) > 0 and a(2) < 0, then the object is slowing down.
If v(2) < 0 and a(2) > 0, then the object is slowing down.
If v(t) < 0 and a(t) < 0, then the object is speeding (but in the West direction).
------------
Working on this assignment, my goal was to teach you.
It was not to work instead of you or to do your job.
Do not forget to post your "THANKS" for my teaching.
If you still have questions, do not hesitate to post them to me.
Happy learning (!)