# If an object is moving at 48 m/s over a surface with a kinetic friction coefficient of u_k=3 /g, how far will the object continue to move?

Jan 6, 2018

It will continue to move about $384 m$ long.

#### Explanation:

In this case, kinetic friction is an opposing force directed opposite to the direction of motion.

For the above statement to be true, the acceleration acting on the object should be opposite (negative).

Forming an equation for frictional force,
$N {\mu}_{k} = M g \cdot \frac{3}{g} = 3 M$
where, $N$ = normal reaction = $M g$
$M$ = mass of the object

$\therefore$ frictional force = $3 M$

According to my second statement,
$3 M = - M a$

So, $a = - 3$m/${s}^{2}$

Now, substituting value of a in,
$v = u + a t$

for an object to come at rest, its final velocity(v) must be = 0
So,
$0 = 48 - 3 t$

$t = 16 s$

Substituting the value of $v , u \mathmr{and} a$ in,
${v}^{2} - {u}^{2} = 2 a s$

We get $s = 384 m$

Hence, the object travels $384 m$ long for $16 s$

Hope this helps !!!!