12- As shown in the figure, a 1.5 kg box is held at rest against a spring with a force constant \( k = 750 \, \text{N/m} \) that is compressed a distance \( d \).**Diagram Explanation:**The diagram illustrates a horizontal setup involving a spring, a box, and a rough patch. The box is placed on the left and is initially at rest. It is compressed against the spring, which is on the right, at an equilibrium position. There is a labeled section indicating the "equilibrium position," and the box is initially at a compression distance \( d \) from it.Directly in the path of the box, labeled with arrows to indicate motion (\( v \)), is a rough patch of surface measuring 6.0 cm in length. This area is the only part with friction when the box slides across it.**Problem Details:**When the box is released, it slides across a surface that is frictionless, except for the rough patch that has a coefficient of kinetic friction \( \mu_k = 0.40 \) and is 6.0 cm in length. If the speed of the box is 2.4 m/s after sliding across the rough patch, determine the initial compression \( d \) (in cm) of the spring.\[ \boxed{\phantom{\_\_\_}} \] cm

Given: The mass 0f box is m=1.5 kg. The force constant is k=750 Nm. The initial compression is d.…

As shown in the figure, a 1.5 kg box is held at rest against a spring with a force constant k = 750 N/m that is compressed a distance d. Equilibrium position d y=0! rough patch '6.0 cm When the box is released, it slides across a surface that is frictionless, except for a rough patch that has a coefficient of kinetic friction u, = 0.40 and is 6.0 cm in length. If the speed of the box is 2.4 m/s after sliding across the rough patch, determine the initial compression d (in cm) of the spring. cm