A nice way to think about the physical meanings of momentum and kinetic energy is in terms of a car travelling along a motorway. If the car has to come to a stop, and this is done by slamming on the brakes and therefore applying a braking force (which we assume is constant), then the momentum of the car is a measure of how long (in time) it takes for the car to stop, while the kinetic energy is a measure of how far (in distance) the car travels before stopping.
In both cases, you get the actual stopping time and stopping distance by dividing the momentum and kinetic energy of the car by the (constant) braking force.