Since the object starts from rest, you can express it's initial velocity in the
period between t=1 and t=2 in terms of the acceleration:v(t)=v0+a∗Δt
v(1)=0+a∗1=a
and substitute this result to the x(t) position equation:
x(Δt)=v0∗Δt+0.5∗a∗Δt2
x(1−>2)=a∗1+0.5∗a∗1=1.5∗a=12
and from here you get:
a=8(m/sec2)
