# If an object is moving at 150 m/s over a surface with a kinetic friction coefficient of u_k=15 /g, how much time will it take for the object to stop moving?

Feb 4, 2016

I found $10 s$

#### Explanation:

Have a look:

Feb 4, 2016

$t = 10 s$

#### Explanation:

${F}_{f} = {u}_{k} \cdot m \cdot g$
${F}_{f} = \frac{15}{\cancel{g}} \cdot m \cdot \cancel{g}$
${F}_{f} = 15 m$ $\text{friction force between object and surface}$
$\text{Kinetic energy of object is zero,if object stops}$
$\Delta {E}_{k} = \frac{1}{2} \cdot m \cdot {v}^{2}$
$\text{Kinetic energy of object turns work .}$
$\Delta {E}_{k} = {F}_{f} \cdot x$
$\frac{1}{2} \cdot \cancel{m} \cdot {150}^{2} = 15 \cdot \cancel{m} \cdot x$
$2250 \cancel{0} = 3 \cancel{0} \cdot x$
$x = \frac{2250}{3} = 750$ $\text{meters}$

$x = \text{blue area}$
$750 = \frac{150 \cdot t}{2}$
$150 \cancel{0} = 15 \cancel{0} \cdot t$
$t = \frac{150}{15}$
$t = 10 s$