A box sliding on a horizontal frictionless surface runs into a fixed spring, compressing

2, The spring would compress twice the length of .

Explanation:

The Spring force is an application of Hooke's law,  and using the law of conservation of energy in a spring system, we can find the relationship between the compression length and velocity.

For a spring system, the conservation of energy can be applied using the formula below;

........................................1

Where k is the spring constant

is the distance

m is the mass and

v is the velocity

We have to make the distance the subject formula to know how it affects the velocity;

.....................................2

from the equation, it shows that the distance () is directly proportional to the velocity (v). This implies that when the distance increases the velocity also increases.

x ∝ v

Therefore when the initial speed is doubled to 2 v it will amount a double increase in the distance which is 2