# Thread: Position function of object moving along x axis

1. ## Position function of object moving along x axis

Okay any help would be appreciated!
Here is the problem: The position function of an object moving along the x axis is given by S(T) = T^3 -6T^2 where T > or equal to zero
During what time intervals is this objecting speeding up and slowing down?
During what time intervals is this object moving to the left and to the right.
What total distrance does this object travel after 5 seconds?

Basically what I have done so far is find the S'(T)= 3T^2 -12T and factored that to 3t(t-4) so I created the interval (0,4) (4,infinity) and I put in test numbers and I did the same for S"(T), and I am looking for changes in the signs of the prime and double primes of these test numbers in the intervals, but it doesn't seem to be leading me to the right answer. Any help would be very appreciated thanks for reading!

2. Originally Posted by Boss_Tycoon
Okay any help would be appreciated!
Here is the problem: The position function of an object moving along the x axis is given by S(T) = T^3 -6T^2 where T > or equal to zero
During what time intervals is this objecting speeding up and slowing down?

Mr F says: Speeding up: Solve S''(T) > 0. Slowing down: Solve S''(T) < 0.

During what time intervals is this object moving to the left and to the right.

Mr F says: Moving to right: Solve S'(T) > 0. Moving to left: Solve S'(T) < 0.

What total distrance does this object travel after 5 seconds? Mr F says: draw a graph, make sure to lable the coordinates minimum turning point. Then you'll see that the answer is |S(4)| + (S(5) - S(4)).

Basically what I have done so far is find the S'(T)= 3T^2 -12T and factored that to 3t(t-4) so I created the interval (0,4) (4,infinity) and I put in test numbers and I did the same for S"(T), and I am looking for changes in the signs of the prime and double primes of these test numbers in the intervals, but it doesn't seem to be leading me to the right answer. Any help would be very appreciated thanks for reading!
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