I know that $ \Sigma F = \Delta mv/\Delta t$. But if we had a marble that moves in a straight line at a constant velocity and colloids with another marble. Because of the law of conservation of momentum, the second marble now had the velocity of the first marble. But what is the force that the first marble applied one the second marble? The collision is almost instantaneous. Wouldn't that make the force in $ \Sigma F = \Delta mv/\Delta t $ insanely large because $ \Delta t $ is so small?
Answer
The force can be surprisingly large, but $\Delta t$ is not zero, and the force is not infinite.
Make some estimates: the duration of the collision is so short that our eyes and brain cannot perceive it. Make an estimate for an upper limit for the duration. (There's no right answer, but a lot of wrong answers. For example, I would think that a duration of 0.1 s would be perceivable, and "wrong". My upper limit should be smaller.)
From this you can get a lower limit on the force.
You can improve your estimate for $\Delta t$. You know the speed of the marble. You can make a guess at the size of the deformation of the ball that occurs during the collision. It's certainly less than one tenth of the radius. Probably less that 1/100 ... (Make your own estimate.) From there calculate a $\Delta t$.
Try this: make a crude model of the force generated when two satellites collided in 2009. The relative speed of the collision is known. The masses and sizes can be found or estimated. Calculate the duration of the collision and the force generated. (They did not collide head-on, so divide by 2 to crudely account for this. :) They also disintegrated. So there the analysis will have flaws. But it's an interesting exercise as long as you keep in mind that it is unrealistic. )
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