Let $F(s)=1.1s+0.03s^{2}$ represent the stopping distance (in feet) of a car travelling at $s$ miles per hour. Calculate $F(30)$ and estimate the increase in stopping distance if speed is increased from $30$ to $31$. Compare your estimate with the actual increase.

$F(30)=$ feet
Estimated increase in stopping distance: feet
Actual increase in stopping distance: feet