falling freely from rest travels 9 m in 1.5 s. What is the free fall acceleration?

Answer 1

free fall distance = X
from rest, starting velocity, Vo = 0
from starting point Xo = 0
time = t
accelaration=a

V = Vo + a*t
X = Xo + Vo*t + 1/2 a*t^2

step-by-step

9 = 0 + 0 * t + 1/2 a*t^2
9 = 1/2 a * t^2
18 = a * t^2
18 = a * (1.5)^2
18 = a * (2.25)
18/2.25 = a
a = 8 m/sec

This is less than typical 9.81m/sec on Earth.
Maybe you're on Venus?

Answer 2

d = (1/2) * g * t^2
9 = (1/2) * g * (1.5)^2
18/(1.5)^2 = g