# If an object is moving at #3 m/s# over a surface with a kinetic friction coefficient of #u_k=20 /g#, how far will the object continue to move?

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To calculate the distance the object will continue to move, we can use the equation:

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

Where:

- (d) is the distance traveled,
- (v) is the initial velocity of the object,
- (\mu_k) is the coefficient of kinetic friction, and
- (g) is the acceleration due to gravity (approximately (9.8 , \text{m/s}^2)).

Plugging in the given values:

- (v = 3 , \text{m/s}),
- (\mu_k = 20 , /g), and
- (g = 9.8 , \text{m/s}^2),

We have:

[d = \frac{(3 , \text{m/s})^2}{2 \cdot (20/g) \cdot (9.8 , \text{m/s}^2)}]

[d \approx \frac{9 , \text{m}^2/\text{s}^2}{39.2 \cdot 20} , \text{m} \approx \frac{9}{784} , \text{m} \approx 0.0115 , \text{m}]

Therefore, the object will continue to move approximately (0.0115 , \text{m}).

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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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