# If an object is moving at #8 m/s# over a surface with a kinetic friction coefficient of #u_k=9 /g#, how far will the object continue to move?

The distance is

Then,

The frictional force is

According to Newton's Second Law

Apply the equation of motion

The distance is

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To find the distance the object will continue to move, you can use the formula:

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

Where:

- ( d ) is the distance traveled,
- ( v ) is the initial velocity of the object (8 m/s in this case),
- ( \mu_k ) is the kinetic friction coefficient (9/g in this case),
- ( g ) is the acceleration due to gravity (approximately 9.8 m/s²).

Plugging in the values:

[ d = \frac{{8^2}}{{2 \cdot 9/g \cdot 9.8}} ]

[ d ≈ \frac{{64}}{{2 \cdot (9/9.8) \cdot 9.8}} ]

[ d ≈ \frac{{64}}{{2 \cdot (0.918) \cdot 9.8}} ]

[ d ≈ \frac{{64}}{{2 \cdot 0.918 \cdot 9.8}} ]

[ d ≈ \frac{{64}}{{17.964}} ]

[ d ≈ 3.56 \text{ 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.

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