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

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?

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