For the derivation of pressure Force if divided by time taken by particle by particle in covering the distance and not time of collision?

Pressure is defined as force acting per unit area. I am not sure why and how come you are saying that for derivation of force, you need to divide force by time taken for the particle to cover a given distance. 

 

I am not sure if you are talking about pressure only, or if you are talking about impulse = F.t  where t refers to the short time interval for which 2 bodies were in contact.