Momentum is the impetus of a moving object, the quantity of motion. Intuitively you can think of it as a measure of how hard it is to stop an object - clearly this depends on its mass and velocity
The gun powder accelerating the bullet in a rifle,
The bow string accelerating the arrow,
The rocket engines accelerating the shuttle,
The fist accelerating the punching bag.
In general impulse is the force applied to a given object with a given mass for a given period of time. This will decide the amount of acceleration, final velocity and the kinetic energy stored in that object. If you know momentum and the mass of the object you do not need acceleration to calculate final velocity. Momentum is conserved. If an object slows down a certain amount of energy is transferred from the object to the environment. This transfer could be in the form of acceleration or deceleration of another object or heat due to friction or collision.