A box sliding on a horizontal frictionless surface runs into a fixed spring, compressing it a distance x1 from its relaxed position while momentarily coming to rest. If the initial speed of the box were doubled, how far x2 would the spring compress?

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

it is called kinetic energy