Solution:

For constant acceleration starting from rest, the displacement \(S = \frac{1}{2}at^2\). The average velocity over time (t) is \(v_{avg} = \frac{S}{t} = \frac{1}{2}at\). The final velocity at time (t) is (v = at). The question asks for the ratio of average velocity to final velocity (assuming "time average velocity" refers to final velocity). Ratio is \(\frac{(1/2)at}{at} = \frac{1}{2}\).