A student is discussing sign conventions used in vertical motion under gravity. She first chooses the downward direction as positive and later repeats the same calculation taking the upward direction as positive.
(i) Explain how the sign of acceleration due to gravity changes between the two conventions.
(ii) For a body released from rest, write the displacement–time relation in each convention and interpret the physical meaning of every term.
(iii) Using either convention, show that the time taken by a body to fall through a height h depends only on h and g, and not on the choice of sign convention.