Question 4

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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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