If Velocity constant will be high then rate of the reaction will also be high.
Threshold energy is the energy which requires by any reactant to converts itself into product so if it is minimum then rate of reaction will be faster.
Mechanism of the reaction gives information about the dependency of the rate of reaction on reactant and product. So it can also change the rate of reaction.
So by seeing this we can say these factors can also make the reaction faster as catalyst does.