Question

If an object is moving at `50 m/s` over a surface with a kinetic friction coefficient of `u_k=8 /g`, how far will the object continue to move?

Answer 1

I found `156m`

Explanation:

Considering that the only force acting on the object will be kinetic friction `f_k`, it will produce an opposite acceleration slowing down the object.
From Newton's Second Law (horizontally):

`-f_k=ma`

and so:
`a=-f_k/m`

Friction will be: `f_k=u_kN`
where, in this case, the normal reaction, `N`, will be equal to the weight `W=mg`;
so:
`a=-(u_kcancel(m)g)/cancel(m)=-8/g*g=-8m/s^2`
With this acceleration you can use:
`color(red)(v_f^2=v_i^2+2ad)`
with `v_f=0` (the object stops)
so you get:
`0^2=50^2-(2*8*d)`
`d=2500/(16)=156m`