# If an object is moving at #150 m/s# over a surface with a kinetic friction coefficient of #u_k=15 /g#, how far will the object continue to move?

The distance is

The coefficient of friction is

Then

So,

According to Newton's Second Law

Therefore,

We apply the equation of motion

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

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

Where:

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

Given:

- (v = 150 , \text{m/s})
- (u_k = 15/g)

Substitute the given values into the equation:

[d = \frac{(150 , \text{m/s})^2}{2 \cdot 15/g \cdot 9.8 , \text{m/s}^2}]

[d = \frac{22500 , \text{m}^2/\text{s}^2}{30/g}]

[d = \frac{22500 \cdot g}{30}]

[d = \frac{22500 \cdot 9.8}{30} , \text{m}]

[d = \frac{220500}{30} , \text{m}]

[d ≈ 7350 , \text{m}]

The object will continue to move for approximately 7350 meters.

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