A block of mass 1 kg , moving along x with speed v _ i =10 ~m / s enters a rough region ranging from x =0.1 ~m to x =1.9 ~m . The retarding force acting on the block in this range is F _ r =- kx N , with k =10 ~N / m . Then the final speed

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A block of mass 1 kg , moving along x with speed v _ i =10 ~m / s enters a rough region ranging from x =0.1 ~m to x =1.9 ~m . The retarding force acting on the block in this range is F _ r =- kx N , with k =10 ~N / m . Then the final speed of the block as it crosses rough region is

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Correct answer: D. 8 ~m / s

aligned & a= F m =-10 x & v d v d x =-10 x aligned ₁₀^ v vdv =-10 _ 0.1 ^ 1.9 xdx aligned & v^2-100 2 =-10 ( 1.9^2-0.1 2 )^2 & v=8 ~m / s aligned

A block of mass 1 kg , moving along x with speed v _ i =10 ~m / s enters a rough region ranging from x =0.1 ~m to x =1.9 ~m . The retarding force acting on the block in this range is F _ r =- kx N , with k =10 ~N / m . Then the final speed of the block as it crosses rough region is

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