Question about Force and Velocity

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Calculating the velocity of a car involved in a collision based on the force exerted during the impact is complex. While it is possible to estimate this velocity, there is no straightforward analytical solution due to the intricacies of plastic deformation in structures. The shape of the dent changes during the impact, complicating the calculations. Non-linear finite element analysis is typically employed in such scenarios, especially in the automotive industry. This method allows for more accurate modeling of the forces and deformations involved in collisions.
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Is there an equation that will find the velocity of a certain force. Namely, if car #2 crashed into car # 1 and figuring the amount of force that caused the dent in car #1 and from that force finding the velocity, of car #2, that caused the dent. Thank you.
 
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Yes and no. There are ways to calculate the velocity of the offending car in this situation. But, there's no closed form analytical solution. This is an area of permanent deformation of structures (called plastic deformation), and the governing equations are incredibly complex because they are dependent on the shape, which keeps changing. In reality, methods called non-linear finite element analysis are used for problems like this. It's widely used in the auto industry and elsewhere.
 

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