waecmaths question:
The distance, d, through which a stone falls from rest varies directly as the square of the square of the time, t, taken. If the stone falls 45 cm in 3 seconds, how far will it fall in 6 seconds.
Option A:
90 cm
Option B:
135 cm
Option C:
180 cm
Option D:
225 cm
waecmaths solution:
$\begin{align} & d\propto {{t}^{2}} \\ & d=k{{t}^{2}}\text{ }\!\!\{\!\!\text{ }k=\text{ proportionality constant }\!\!\}\!\!\text{ } \\ & \text{When d}=45cm\text{ }t=3 \\ & 45={{3}^{2}}k \\ & k=5cm/s \\ & \text{In 6 seconds, the distance covered by the stone will be } \\ & d=5\times {{6}^{2}}cm=180cm \\\end{align}$
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