A block of mass 1 kg is given a horizontal velocity of 4 m/sec along a horizontal surface which provides a
coefficient of friction of 0.4 (both kinetic and static) . the block strikes a fixed horizontal ideal spring of force
constant 6N/m after travelling a distance of 0.25 m along the horizontal surface .
Find the final displacement of the block from its starting point.
If your answer can be expressed as a/b where a and b are positive coprime integers then find the value of (a*b) + 30
Details And Assumptions
assume that the natural length of the spring is sufficient for the block to fully come to rest ( neglect any collision )
friction is present everywhere on the horzontal surface (even on that surface too where the spring is present)
assume Acceleration due to gravity = 10 SI units
The spring is ideal (massless , does not possess its own kinetic energy)
the answer should be calculated in SI units only .