The first two depend on temperature.
The third may be looking for the answer surface area, but this is not about the reaction happening faster because the ingredients are mixing better (like why flammable powders react so fast in oxygen). In this case, it is easier for the vegetables to cook because the temperature in the vegetable can reach the temperature in the broth because of enhanced heat transfer. The effect is based on the surface area to volume ratio and is a heating effect. Ultimately, I would say temperature because of enhanced heat transfer.