# If an object is moving at 4 m/s over a surface with a kinetic friction coefficient of u_k=12 /g, how far will the object continue to move?

Dec 13, 2015

Its a simple application of kinematics.

#### Explanation:

Normal force in this scenario is $N = m g$
Frictional force $f = \setminus \mu m g = {u}_{k} m g$
${u}_{k} = \setminus \frac{12}{g}$, therefore $f = 12 m$, where the $g$s get cancelled.
Acceleration $a = 12 \frac{m}{s} ^ 2$
Therefore using the kinematic formula
${v}^{2} - {u}^{2} = 2 a s$, where $s$ is the distance traveled, $u$, $v$ are the initial and final velocities and $a$ acceleration.
$u = 4 \frac{m}{s}$
$v = 0$
$a = 12 \frac{m}{s} ^ 2$
Therefore, $s = {u}^{2} / \left\{2 a\right\}$
substituting values given we get $s = \frac{4 \setminus \times 4}{2 \setminus \times 12} = \frac{16}{24} = \frac{2}{3} = 0.667 m$