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A penguin weighing 300 N slides across an icy floor with an inital speed of 6.38 m/s and slides 32.2 m before coming to a stop. Find the frictional force between the penguin and the floor and find the coefficient of kinetic friction. Use g=10m/s^{2}

The first thing I did was to find the mass of the penguin, which is 30 kg. Now I use the equation [itex]{v}^2={v_i}^2+2a\Delta x[/itex]. I come up with:

[tex]6.38^2+64.4a=0\implies a=-.632 m/s^2[/tex]

Now to find the force, I multiplied by the mass 30 kg and came up with the frictional force as -18.96 N. To find the coefficient of kinetic friction from here, I took -18.96 and divided it by 300 N, coming up with -.0632.

Are my steps / results correct?

Thanks,

Alex