The acceleration is here present because of friction.
Our acceleration here would be -mu*g.
Where mu is the coefficient of friction and g is the gravitational acceleration.
Hence acceleration a=-mu*g=-xg
vdv/dx=-xg
Hence
v^2/2- 510^2/2=-g/2*x^2
Now v is zero so
510=x√g
x=510/√g=161.27
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