A spring with a constant k stores potential energy when it is compressed a distance x. That potential energy is given by the formula:

On the other hand, that potential energy comes from the kinetic energy of the block. If the block has a mass m and an initial speed v, then its kinetic energy is equal to:

Substitute k=955 N/m and x=0.10 m to find the potential energy stored in the spring after the collision:

Isolate v from the equation for the kinetic energy of the block:
![v=\sqrt[]{(2K)/(m)}](https://img.qammunity.org/2023/formulas/physics/college/70u0lwqi9eg4id6uo44t1ralai6wfcdray.png)
Since all the potential energy of the spring corresponds to the initial kinetic energy of the block, substitute K=4.775J and m=1.70kg to find the initial speed of the block:
![\begin{gathered} v=\sqrt[]{\frac{2\cdot4.775J}{1.70\operatorname{kg}}} \\ =\sqrt[]{(9.55J)/(1.70kg)} \\ =\sqrt[]{5.6176\ldots(m^2)/(s^2)} \\ =2.37(m)/(s) \end{gathered}]()
Therefore, the initial speed of the block is:
