The graph below shows the position s = f(t) of a body moving back and forth on a

Question

The graph below shows the position s = f(t) of a body moving back and forth on a coordinate line, (a) When is the body moving away from the origin? Toward the origin? How do you find (a), and why is that the answer? The answers given list the intervals when the function moves towards or away from the t - axis. Was the "origin" referred to in the question talking about the t - axis not the actual origin at (0, 0)? Ans. Moving towards the origin on: (1, 2) U (7.7, 7) Moving away from the origin on: (0, 1) U (2, 5.7) U (7, 10)

Explanation / Answer

The function is moving away from origin from (0,1) U (7,10) U (2,5.7)

The function is moving towards the origin fro (1,2) U (6,7)

The movement of the function is to be considered with respect to the line y=0, i.e, the x-axis. When the graph of the function is getting inclined or moving towards the x-axis, then it is considered to travelling towards the origin whereas when the function is moving away from the x-axis then it is considered as travelling away from the origin.

The interval is to be taken until the direction changes. For example in the above question the functions is moving away from the origin from (0,1) and at x=1 the function changed its direction and therefore it's not considered as a movement away from the origin after x=1

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