20. Five marks exercise problems V

The distance \(S\) an object travels under the influence of gravity in time \(t\) seconds is given by \(S(t) = \frac{1}{2} gt^2 + at + b\) where (\(g\)) is the acceleration due to gravity), \(a\), \(b\) are constants. Check if the function \(S(t)\) is one-to-one.