Problem:
A particle moves along a straight line such that a=[-4x^(-.5)] ft/s^2 where we measure x in feet and t in seconds. When t=5 s the particle is located at x=10 m and moves with velocity v=14m/s. Determine the particle's velocity as a function of position.
Requirement:
Question: Evaluate the particle's position when the velocity of the particle is (a) v=7.0m/s, (b) v=3.5m/s, and (c) v=0.
Note: Please provide reasons to support your answer.