# If an object is moving at 3 m/s over a surface with a kinetic friction coefficient of u_k=5 /g, how far will the object continue to move?

May 8, 2016

Here KE of the object = Work done against the force of kinetic friction
So ${u}_{k} \times m \times g \times d = \frac{1}{2} \cdot m \cdot {v}^{2}$
Where ${u}_{k} = \frac{5}{g}$
$m = \text{mass",v="velocity}$
g="acceleration due to gravity=9.8m/s^2
$d = \text{distance traversed}$

${u}_{k} \times m \times g \times d = \frac{1}{2} \cdot m \cdot {v}^{2}$
$\frac{5}{g} \times \cancel{m} \times g \times d = \frac{1}{2} \cdot \cancel{m} \cdot {v}^{2}$
$d = {v}^{2} / 10 = {3}^{2} / 10 = 0.9 m$