A block of mass 10.2
Kg is moving horizontally with a constant velocity of 4.428 m / s . It
encounters an unstretched spring with a spring constant of 200 N /m and
also the floor stretch BC ( as shown ) having a coefficient of friction
0.5, simultaneously. The length of the stretch BC is 1 m . Find the distance
of the point where the velocity of the block becomes zero for the first
time, measured from C. a ) 0.78 m 

Let x be the elongation of the spring ; M , the mass of the block ; N_{a} the normal reaction on the block ; k the coefficient of spring and m the coefficient of friction. Since there is no vertical motion, the weight of the block must equal its normal reaction. N_{a}
= M g = 10.2 ( 9.81 ) = 100.06 N . From the free body diagram of the block, its equation of motion is given by 
m N_{a } k x = M a 10.2 ( a ) =  50  200 x
