Why do physical processes... take time? A spoon is dropped in a vat of acid. The outside of it melts away... over time.
A pill is swallowed and dissolves in a stomach... over time.
A flammable gas is lit, and the flame travels from the ignition point and consumes the remaining mixture, from the inside out.
A car falls off a boat into the ocean and rusts... over time.
Why does it take time though? If for example, something requires enough energy to reach the "activation energy" to start a reaction or process, why isn't it "instant" (or at the very least nearly instantaous? Why does anything take time?
Perhaps my examples are imperfect and can be explained away with "enough stochastic particles randomly flying and bouncing around eventually interact but some have longer paths and therefor spread the reaction over time". Like enough unreacted salt water touching rusting metal, and then more flows in and reactions, and so on.
But it feels like there are examples that can thought up that aren't explained that way. Though at the moment, I'm having trouble giving more.
 A: The examples all involve both diffusion processes and reaction rates. When something diffuses particles move along random walks, spreading out as time passes (with a mean displacement $\sim D\sqrt{t}$ where $D$ is the diffusion coefficient). In the case of chemical reactions they occur at a rate that depends on how many reacting molecules get together with enough energy to get over a potential barrier - the rate will depend on temperature (as per the Arrhenius equation) as well as concentrations (how often do the molecules bang together). 
So why are diffusion coefficients and reaction rates finite? The relevant issue is that the molecules involved move at a finite speed and has a finite spacing. The velocity has to be below lightspeed, and in practice will be far, far lower and set by temperature ($v \sim \sqrt{3RT/M}$ where $R$ is the gas constant and $M$ the molar mass). The density of ordinary matter is somewhere between one and a few thousand kilograms per cubic meter. That means that if the density is $\rho$ the typical distance will be $L \sim (\rho/\mu)^{-1/3}$ if $\mu$ is the mass of a molecule ($M=N_A \mu$). So the natural timescale of anything happening will be $$\tau =L/v \approx (\rho/\mu)^{-1/3}\sqrt{\frac{N_A \mu}{3RT}}=\sqrt{\frac{N_A\mu^{5/3}}{3RT\rho^{2/3}}}.$$
So my answer is: physical processes take time because densities and temperatures are low compared to the masses of molecules or other reacting entities. When you get to very high energies and densities things go fast.
A: An interesting way to think about time is if we consider the concept of change. All the examples you’ve mentioned before involve some form of change. If our universe were static like suppose the world in a photograph where no spatial position co-ordinates, nor momentum of any subatomic particles change, that is they remain the same. But what we doobserve in our universe is that position and momentum of matter/fields, etc. do change. As the acid molecules interact with the ones in the spoon there is a change and interaction of forces that result in some form of movement of molecules and evolution of the chemical reaction etc. This steady passage of change is the human construct we call time.
A point to note is that there is nothing called nearly instantaneous, things either move/change or they don’t. The reason suppose it takes time for an ignition because there needs to be a certain sequence of energy transfers and movements of molecules for what we see as an ignition to develop. And now as we established that change exists the sequence in these steps and a finite duration due to finite speeds in spatial movements is what makes reactions not instantaneous, but rather, requiring time.
