# If an object is moving at #22 m/s# over a surface with a kinetic friction coefficient of #u_k=11 /g#, how far will the object continue to move?

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To find how far the object will continue to move, we can use the equation for the distance traveled under constant acceleration due to friction:

[ d = \frac{{v^2}}{{2 \mu_k g}} ]

Given:

- Initial velocity, ( v = 22 ) m/s
- Kinetic friction coefficient, ( \mu_k = \frac{11}{g} )
- Acceleration due to gravity, ( g = 9.81 ) m/s²

Substitute the values into the equation:

[ d = \frac{{(22)^2}}{{2 \times \frac{11}{9.81} \times 9.81}} ]

[ d = \frac{{484}}{{2 \times \frac{11}{9.81}}} ]

[ d = \frac{{484 \times 9.81}}{{2 \times 11}} ]

[ d = \frac{{4744.04}}{{22}} ]

[ d \approx 215.64 , \text{m} ]

So, the object will continue to move approximately 215.64 meters.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- An object with a mass of # 4 kg# is lying on a surface and is compressing a horizontal spring by #8 cm#. If the spring's constant is # 2 (kg)/s^2#, what is the minimum value of the surface's coefficient of static friction?
- An object with a mass of #9 kg# is on a plane with an incline of # - pi/4 #. If it takes #15 N# to start pushing the object down the plane and #5 N# to keep pushing it, what are the coefficients of static and kinetic friction?
- An object, previously at rest, slides #4 m# down a ramp, with an incline of #pi/3 #, and then slides horizontally on the floor for another #5 m#. If the ramp and floor are made of the same material, what is the material's kinetic friction coefficient?
- An object with a mass of #6 kg# is on a plane with an incline of #pi/12 #. If the object is being pushed up the plane with # 6 N # of force, what is the net force on the object?
- Do action and reaction pairs cancel one another?

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