For which of the following situations would a linear function be a reasonable choice for a mathematical model?
-the success rate of field-goal kicking as a function of distance from the goal post
-the number of people who have heard something as a function of time after the first person is told
-stopping distance (in a car) as a function of speed

The third option is the best fit for the application of a linear model.

In the first option, there is likely to be a correlation but it cannot be a linear one as goals are missed even from inside the keeper's box.

In the second option, it is safe to assume that each person will at least 2 other so this will follow an exponential model.

In the third option, the stopping distance is given by the equation of motion:
s = ut + 1/2 x at²
And this shows that the distance varies linearly with speed.