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Suppose we have two balls or two boxes colliding or we hit a ball at rest, does this mean that the force and acceleration at the time of collision are close to infinity?

Because at the time of collision the speed changes from 0 to specific speed in a very short time ≈ 0, so the acceleration is close to infinity, and Because the acceleration approaches infinity, the force approaches infinity, according to the second Newton's law;

Is what I'm saying true?

Aymen
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    You may try also the physics.stackexchange – uniquesolution Dec 29 '23 at 22:30
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    As you approximate the exchange of momentum on shorter and shorter time scales, i.e. $\Delta t \to 0$, the approximate force $F \to \infty$, but these tend to balance out: $$ J = \Delta p = \frac{F}{\Delta t}. $$ Are you familiar with impulse (change of momentum)? – Sammy Black Dec 29 '23 at 22:32

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This question actually puzzled the great Galileo. enter image description here The force may indeed become very large in a very short amount of time, but the product of the force and the time duration of the collision, namely $F\Delta t$ (it is $\Delta t$ because it happens in a very short interval of time) - which is called the impulse, is equal to the change in momentum, so that if the force grows very large, the time it acts grows very small.

[(1) Galielo - Dialogues concerning two new sciences]

uniquesolution
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Just because the time is nearly zero means the acceleration is infinity because the velocity is acually also near zero what you're trying to say here is exactly the same as $a=\frac{dv}{dt}$ which is just the definition of acceleration the rate of change of velocity with respect to time so the ratio is constant after x seconds even of x approaches zero

Ashh
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