It is said that force is an interaction that causes an object to accelerate. It is measured in newtons. $1$ N of force causes an object with a mass of $1$ kg to accelerate at $1$ m/s². Now let's imagine a box sliding on frictionless surface and hitting a standing box. Standing box will accelerate. But their interaction will last extremely short amount of time. Isn't the length of time of them touching each other approaching zero? If it is, isn't the acceleration approaching zero?
Intuitively we know it will move, but mathematically it confuses me.
Thanks for answers!