Question

If an object is moving at `18 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

`x=13.5 " meters"`

Explanation:

`"1- Find the friction force :"`
`F_f=u_k*m*g" "u_k=12/g`

`F_f=12/cancel(g)*m*cancel(g)`

`F_f=12m`

`"2- Find deceleration using Newton's law :"`

`F_f=m*a`

`12cancel(m)=cancel(m)*a`

`a=12 m/s^2`

`"3- Find distance using the formula :"`

`v_f^2=v_i^2-2*a*x`

`"where :"`

`v_i:"initial velocity"`
`v_f:"final velocity=0"`
`a:"deceleration"`
`x:"distance"`

`0=18^2-2*12*x`

`324=24*x`

`x=324/24`

`x=13.5 " meters"`