# If an object is moving at 10 m/s over a surface with a kinetic friction coefficient of u_k=5 /g, how much time will it take for the object to stop moving?

Jul 10, 2016

2 seconds.

#### Explanation:

This is an interesting example of how cleanly most of an equation can cancel out with the correct initial conditions. First we determine the acceleration due to friction. We know that the frictional force is proportional to the normal force acting on the object and looks like this:
${F}_{f} = {\mu}_{k} m g$

And since $F = m a$:
${F}_{f} = - {\mu}_{k} m g = m a$
${\mu}_{k} g = a$

but plugging in the given value for ${\mu}_{k}$...
$\frac{5}{g} g = a$
$5 = a$

so now we just figure out how long it'll take to stop the moving object:
$v - a t = 0$
$10 - 5 t = 0$
$5 t = 10$
$t = 2$ seconds.