Question

a moving cart hits a spring, traveling at 5.0 m/s at the time of contact. at this instant the cart is motionless by how much is the spring compressed

Answer 1

This state of motionlessness occurs because all of the kinetic energy in the car is absorbed by the spring in the form of elastic potential energy. The mathematical representation is:
1/2 mv² = 1/2 kx²
25m = kx², where m is the mass of the cart, k is the spring constant and x is the spring's extension.