a)
Since the force of 25 N is applied by a distance of 10 meters, we can calculate the work done:
[tex]\begin{gathered} W=F\cdot d \\ W=25\cdot10 \\ W=250\text{ N} \end{gathered}[/tex]
Then, if all the energy is kinetic energy, we can calculate the box speed:
[tex]\begin{gathered} E_k=\frac{mv^2}{2} \\ 250=\frac{10\cdot v^2}{2} \\ 5v^2=250 \\ v^2=50 \\ v=7.07\text{ m/s} \end{gathered}[/tex]
b)
The box slides up the hill, so part of the energy is now potential energy:
[tex]\begin{gathered} E_p=m\cdot g\cdot h \\ E_p=10\cdot9.8\cdot2 \\ E_p=196\text{ J} \end{gathered}[/tex]
The remaining kinetic energy (250 - 196 = 54 J) will be converted into elastic potential energy of the spring:
[tex]\begin{gathered} E_{ep}=\frac{1}{2}kx^2 \\ 54=\frac{1}{2}\cdot k\cdot2.5^2 \\ 6.25k=108 \\ k=17.28\text{ N/m} \end{gathered}[/tex]
