Well according to the equation that relates the two.
F = M • a
A = acceleration = velocity/time
Velocity = displacement/time.
Assuming that there is no change in the displacement, in other words, one is pushing an object in one direction only.
Then distance can equal displacement.
Thus to keep pushing on an object in a straight line at a certain acceleration, maintaining the same speed over each time interval. You need to be applying a constant force.
The greater the distance that you need to push the object for at a specific acceleration the greater the force.
