# If a #3/2 kg# object moving at #3/4# #ms^-1# slows to a halt after moving #5/8 m#, what is the coefficient of kinetic friction of the surface that the object was moving over?

##### 1 Answer

#### Answer:

First find the acceleration, then use it to find the magnitude of the frictional force, and use that to find the coefficient of friction.

#### Explanation:

First find the acceleration:

Rearranging to make

The negative sign just shows that the object is decelerating - its acceleration is in the opposite direction to the initial velocity.

Now to find the frictional force:

The frictional force is given by

Rearranging to make the frictional coefficient the subject:

(frictional coefficients have no units, since they are ratios of forces)

(note: technically, a coefficient of friction is *between* two bodies, not a property of the surface alone)