A block sliding along a horizontal frictionless surface with speed v collides with a spring and compresses it by 1.0 cm . What will be the compression if the same block collides with the spring at a speed of 4v

The  compression is  

Explanation:

From the question we are told that

     The first velocity is  v

     The  compression of the spring is  

      The  second velocity is  4v

Generally according to the law of  energy conservation

   The  kinetic energy of the block is equal to the energy stored in the spring that is  

For  first speed

=>  

=>  

For second  speed

=>    

substituting for k

=>    

=>

=>  

. west