Since plants absorb minerals, like potassium, calcium, sulfur, etc. in their ionic form, like K+, NO3-, SO42-, Ca2+, they need to absorb them actively. Since these ions are charged, they have difficulty while passing through the plasma membrane. Hence, plants need to expend energy in order to transport them. For this, they use ATP and membrane transporter proteins. These transporters transport ions across cell membrane with an accompanying ion (H+) so as to maintain electrochemical gradient. As a result (partly), these transporters are highly selective for the ions they carry. For example, a K+ transporter will not transport SO42- or another ion. See this answer to see how transporters achieve this selectivity.
The above part explains how ions are transported in plants. Now, lets come to the main question i.e. why some ions are transported faster than others. Well, there is no definitive answer to this (at least none that I know of). But I can think of two possible reasons for this (using only the examples of K+, Ca2+, NO3- and SO42-):
Magnitude of Charge: one fact here is that both K+ and NO3- have a charge of $\pm$1, whereas Ca2+ and SO42- have a charge of $\pm$2. So what? This makes their transport a bit more difficult. For example, to transport K+ across the membrane, the transporter would antiport 1 H+ for 1 K+, whereas a similar antiporter would transport 2 H+ out to bring 1 Ca2+ in. Obviously, this does not explain the difference between ions with same charge, which the following point seems to do.
Requirement: one of the most important points to keep in mind here is the difference in requirements of different ions by the plant. This is why plant macronutrients (i.e. required in large quantities) have been divided into primary macronutrients (N, P, K) and secondary macronutrients (all others, including Ca, S, Na). As you see, nitrogen and potassium are mostly the limiting factors of crop production. This is why plants require them in large quantities, and hence try to absorb them as fast as possible. This, partly again, explains why K+ and NO3- (the only artificial nitrogen source other than NH4+) are absorbed faster by plants while Ca2+ and SO42- are absorbed slowly.