WAEC Mathematics 2016 Paper

Concept:Direct variation with a square means $d \propto t^2$, so we use $d = k t^2$, where $k$ is a constant.Explanation:The stone falls from rest, so the distance $d$ varies directly as the square of the time $t$.This gives the equation $d = k t^2$.When $t = 3$ seconds, $d = 45$ cm.Substitute these values into the equation:$45 = k \times (3)^2$$45 = 9k$$k = \frac{45}{9} = 5$.So the relationship is $d = 5t^2$.Now find the distance when $t = 6$ seconds:$d = 5 \times (6)^2$$d = 5 \times 36$$d = 180$ cm.Answer:The stone falls $180$ cm in 6 seconds, so the correct option is C. $180$ cm.