Question

If an object is moving at `7` `ms^-1` over a surface with a kinetic friction coefficient of `u_k=2/g`, how far will the object continue to move?

Answer 1

The distance traveled is `24.5` `m`.

The mass cancels out and so does the value of 'g', and we can use the calculated acceleration and the fact that the final velocity is 0 to find the distance traveled.

Explanation:

The force causing the deceleration will be the frictional force, given by `F_"frict"=muF_"norm"`, where the normal force `F_"norm"=mg`, so `F_"frict"=mumg`.

The acceleration of the object will be given by `a=F_"frict"/m=(mumg)/m`

The mass cancels, which is convenient since we have not been told its value: `a=mug=2/g xx g`

The g also cancels, so that the acceleration is just equal to `2` `ms^-2`. Since it is in the opposite direction to the initial velocity, we can write this as `-2` `ms^-2`.

Now we can use `v^2=u^2+2as`. The object comes to rest, so the final velocity, `v=0` `ms^-1`.

`0^2 = 7^2 +(-2)s`

Rearranging:

`s=49/2=24.5` `m`