In the xy-plane, the line determined by the points (2,k) and (k, 32) passes through the origin. Which of the following could be
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Part A
Given that
Then,
For
, then
Thus,
For
, we have
Part B
Recall that from part A,
Now, at initial position, t = 0 and
, thus we have
and when the velocity drops to half its value,
and 
Thus,
Thus, the distance the particle moved from its initial position to when its velocity drops to half its initial value is given by
Given that
Then,
For
Thus,
For
Part B
Recall that from part A,
Now, at initial position, t = 0 and
and when the velocity drops to half its value,
Thus,
Thus, the distance the particle moved from its initial position to when its velocity drops to half its initial value is given by