Moving or rotating objects have momentum. Momentum is a numerical representation of the motion of an object.
The momentum of an object that is moving linearly can be calculated by multiplying the object's mass and velocity.

momentum = mass × velocity

momentum = m × v

Momentum and impulse

The impulse experienced by the object equals the change in momentum of the object.
The result of the force acting for the given amount of time is that the object's mass either speeds up or slows down.

force × given amount of time = change in momentum(impulse)

Therefore, the following equation is established.

impulse = change in momentum

\[ F \Delta t = \Delta mv \]

At this time, the 'force(F)' component is called 'impact force.'

\[ impact\; force = \frac { change\; in\; momentum }{ time } \]
\[ F = \frac { \Delta mv }{ \Delta t } \]

The reason why the pillow fight is not so painful

When the momentum is constant, the time interval and the impact force are inversely proportional.
Collision with fluffy objects prolongs impact time. Therefore, the longer the time, the weaker the impact force.