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 .

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