A particle is projected from a point O O\,O along a straight horizontal line with speed k m s−1k\text{ m s}^{-1}k m s−1, where k>0k>0k>0. It moves with constant acceleration -2 m s-2 until it returns to OOO. The greatest displacement of the particle from O O\,O is 36 m.
Show that the time at which the particle changes direction is k2\dfrac{k}{2}2k seconds.
Determine the value of kkk.
Find the total time taken for the particle to return to OOO.