What makes us move in time? Time is considered to be a dimension, and we are moving at certain rate in one direction in time. What force makes us move in time? I mean it must be ether time moving or us moving in time so there has to be some force that 'pushes'/'pulls'? Was this 'time inertia' acquired during big bang, or nothing is moving and I am just being silly? 
 A: What makes heat move from hot to cold? Entropy. How can you calculate entropy microscopically? Start counting states! 
What makes the universe change irreversibly from yesterday to tomorrow? Start counting states! 
A: Take a landscape. It can be modeled by a function f(x,y,z). If all the derivatives, df/dx, df/dy, df/dz are zero, the landscape is flat to infinity  and nothing interesting exists in the landscape.
If one of the derivatives is different than zero, then we perceive a shape, and generally a landscape has a shape. As  an example, suppose that we have a cone for this landscape, and there exists a funny "life" that exists in the distance from the center of the cone . All in one snapshot for us, birth is at the cone, middle age is some distance and death is where f is zero. 
In a similar manner we can think of time for each of us as starting at birth making a four dimensional shape and ending at death. Another life form will see us as I explain in the example with the cone. Thus time as a dimension for human perception is a df/dt. If nothing changed, there would be an uninteresting landscape .
Now we have developed means of studying what at first is a fourth dimension time axis, because all matter exists and has a df/dt in the four dimensional space. We have concluded from our observations that time has an arrow, i.e. one cannot "move" in the negative direction, from observing how nature behaves thermodynamically and microscopically. Entropy always increases , and that defines an arrow of time independent of the human perception. 
The "motion" of time is the motion of our perception. When we look at a three dimensional landscape we can perceive it from zero to infinity. The landscape is not moving. With time we are at a specific time=t_0 sequentially and the four dimensional landscape opens to our perception in slices ultimately controlled by the rate of increase in entropy in our surroundings. The "force" is the usual statistical mechanics and quantum statistical mechanics that rules the nature of matter.
