Newton's 2nd Law: Why is this Mass times Acceleration?

Question

I am a physics student that just started to learn the subject, and I came over to this section about Newton's second law. It says, that force is mass times acceleration, but why is it like this, without other parts like velocity? For example, in space, there are two objects flying with constant velocity, and no forces acting upon them. If they collide, will there be no force acting there, as Newton's 3rd law is on forces interacting, not just velocity and mass?

Answer 1

but why is it like this, without other parts like velocity?

Newton’s second law actually states that a force acting on an object is equal to it’s rate in change of momentum. That is,

$$\vec F = \frac{d \vec p}{dt} = \frac{d (m \vec v)}{dt} = m \frac{d \vec v}{dt} = m \vec a$$

So you can see that velocity is very much a part of this law.

If they collide, will there be no force acting there, as Newton's 3rd law is on forces interacting, not just velocity and mass?

Newton's third law states that for a force applied by one object on another object, then the second object exerts back an equal force on the first one but opposite in direction. This idea was used by Newton to derive the law of conservation of momentum. In other words, the momentum of a system will always remain the same. So in your example of two objects colliding

$$m_1 v_1 + m_2 v_2 = constant$$

before they interact and after they interact.

Answer 2

If the objects collide, there will definitely be forces acting - each object exerting an equal and opposite force on the other.

Each one will undergo a change in velocity (obviously). That change in velocity is, of course, acceleration, and the forces involved will be proportional to that change in velocity times the mass of object in question.

The velocity of each object isn't directly in the F = ma equation, and that may feel counterintuitive, but it will have an impact on the numbers involved. The higher the velocities of a given collision the higher the forces will be and thus the larger the change in velocity (acceleration).