The distance, d, through which a stone falls from rest varies directly as the square...

WAEC 2016

The distance, d, through which a stone falls from rest varies directly as the square of the time, t, taken. If the stone falls 45cm in 3 seconds, how far will it fall in 6 seconds?

A. 90cm
B. 135cm
C. 180cm
D. 225cm

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Correct Answer: Option C

Explanation

d \(\alpha\) t²

d = t² k

where k is a constant. d = 45cm, when t = 3s; thus 45 = 3² x t

k = \(\frac{45}{9}\) = 5

thus equation connecting d and t is d = 5t²

when t = 6s, d = 5 x 6²

= 5 x 36

= 180cm

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