What is the relationship between distance and acceleration?

What is the relationship between distance and acceleration?
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displacement (s)=initial velosity(u)*time(t) + 1/2 acceleration (a)*(t^2) from a stationary start this simplifies to s=1/2a(t^2) this arises from the fact that a is the second integral of s with respect to time eg. d/dt=s: x=st+u (velosity v=distance*time +initial velosity) (d^2)/d(t^2)= s(t^2)/2+ut+d=a as we are measuring displacement and not position, the constant of integration d drops, leaving a=s(t^2)/2+ut : s=ut+1/2a(t^2)
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