To simulate car accidents, auto manufactrers study the collisions of moving cars with mounted springs of differnet spring constants. Consider a typical simulation with a car of mass 1000 kg moving with a speed 18.0 km/h on a smooth road and colliding with a horizontally mounted spring of spring constant `6.25xx10^(3)N m^(-1)`. What is the maximum compression of the spring ?

Explanation

At maximum compression `x_(m)`, the potentia energy V of the spring is equal to the kinetic K of the moving car from the principle of conservation of mechanical energy.
`K=UrArr(1)/(2)mu^(2)=(1)/(2)kx_(m)^(2)rArrx_(m)=usqrt((m)/(k))rArrx_(m)=usqrt((m)/(k))`
We obtain `x_(m)` = 2.00m