# How does the velocity of an object change to force in a collision?

My apologies in advance for so rookie question.

Stage:

An object (hereinafter A) traveling through space (suppose no pollutant forces) at a constant velocity wrecks against another object (hereinafter B) at rest.

Considerations:

A is going to lose velocity, therefore a negative acceleration has been applied on it.

B is going to acquire velocity, therefore a acceleration has been applied on it.

As an acceleration has been applied on both objects, I affirm that a force has been applied on them.

Question:

What and how does the velocity of object A transform into a force when impacting?

I have not seen any magnitude which has ML/T dimension which can explain me this event.

( I suppose there is not one force before impact because A has no acceleration )

Thank you.

• A question with the header "Force, acceleration & velocity" is likely to be put on hold as not having been researched. It might have a better chance as "How does the velocity of an object change to force in a collision?" Nov 19, 2016 at 12:32
• It's a bit of a leap of logic to say that velocity is converted to force. (Velocity is not converted to force.) Nov 19, 2016 at 22:23

According to Newton, the fundamental quantity of motion is momentum, and force changes momentum. The idea of acceleration and its relationship to force comes from change in momentum.

Both of your objects have an initial momentum, $mv$, with units $$kg\frac{m}{s}.$$ and that is the ML/T magnitude you seek.

During the time of the collision, the rate of change of momentum of each object has units $$\frac{kg\frac{m}{s}}{s}.$$ This rate of change is proportional to the force, and is equal to $ma$

If your question also pertains to how force arises physically from the collision of two objects with velocities, just remember that contact forces are electrostatic in nature.   So the objects get compressed against the forces of electrostatic repulsion, and the kinetic energy they had is divided between temporary storage in the fields between electrons during elastic deformation, and transfer to thermal energy during permanent deformation.

When body A collides with B, as you guessed it right, it loses velocity as it deaccelerates. But what causes the body to deaccelerate in such a way? Repulsive atomic forces. When atoms/molecules of two bodies come sufficiently close in contact with each other, a repulsive force between atoms acts in this way. As for how this velocity is converted ito force, by Newton's Second Law, $$\vec{F} = \frac{d\vec{p}}{dt}$$ where,

$\vec{F}$ is the force acting on the body, $\vec{p}$ is the momentum of the body and $t$ is the time.

Newton's third law tells you that the V two objects are subjected to equal and opposite forces.
These forces will vary in magnitude $F(t)$ during the collision and the important parameter is the impulse $\int_{\rm collision} F(t)\; dt$ that is applied to the colliding objects as this is equal to the change in momentum (mass $\times$ velocity$of the objects. This comes from Newton's second law which states the rate of change of momentum$p$of a body is equal to the force applied to it$F=\frac{dp}{dt} \Rightarrow \int_{\rm collision} F(t)\; dt =\int_{\rm collision} dp\$.

So for the two colliding bodies the magnitude of the forces acting on them is the same, the magnitude of the impulse acting on them is the same and the magnitude of the change in momentum is the same.

As there are no external forces acting on the two colliding bodies then the change in momentum of one body is equal in magnitude but opposite in direction to the change in momentum of the other body.
If the momentum changes so the velocity must change.