<image>According to the observation and prediction by the Meteorological Center: The sandstorm that occurred in $$M$$ is moving continuously in the due south direction, and the function graph of its moving speed $$v(km/h)$$ with respect to time $$t(h)$$ is shown in the figure below. Drawing a perpendicular line $$l$$ to the horizontal axis through the point $$T(t,0)$$ on the line segment $$OC$$, the area of the part of the trapezoid $$OABC$$ on the left side of the line $$l$$ represents the distance $$s(km)$$ covered by the sandstorm within $$t(h)$$.
$$(1)$$ When $$t=4$$, find the value of $$s$$;
$$(2)$$ Express the relationship between $$s$$ and $$t$$ using a mathematical formula.