Given a radioactive particle that encounters a shielding barrier, it is known to decelerate and come to rest within the shielding in 6 microseconds (6 ?s). In this example, presume the distance (d in microns (?m)) the particle will travel in the time period after hitting the shielding is given by the following equation.

Given the bounds t₀ = 0 ?s and t_max = 6 ?s

= 18t + 108t