Question

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?

Answer 1

Its a simple application of kinematics.

Explanation:

Normal force in this scenario is `N= mg`
Frictional force `f=\mu mg=u_kmg`
`u_k=\frac{12}{g}`, therefore `f=12m`, where the `g`s get cancelled.
Acceleration `a=12m/s^2`
Therefore using the kinematic formula
`v^2-u^2=2as`, where `s` is the distance traveled, `u`, `v` are the initial and final velocities and `a` acceleration.
`u=4 m/s`
`v=0`
`a=12m/s^2`
Therefore, `s=u^2/{2a}`
substituting values given we get `s={4\times4}/{2\times12}=16/24=2/3=0.667m`