# If an object is moving at #4 ms^-1# over a surface with a kinetic friction coefficient of #mu_k=16 /g#, how far will the object continue to move?

The object will decelerate (accelerate in a direction opposite to its velocity) and stop after

If there were no friction, the object would keep moving together. Since there is friction, there is a net unbalanced force acting that will cause the object to slow and stop.

Summarising what we know and what we need to know:

Substituting into Newton's Second Law:

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I found

with this information we can use the kinematic relationship:

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To calculate 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 (4 m/s in this case),
- ( \mu_k ) is the coefficient of kinetic friction (0.16 in this case),
- ( g ) is the acceleration due to gravity (approximately ( 9.81 , \text{m/s}^2 )).

Substitute the values into the formula and solve for ( d ).

[ d = \frac{{(4 , \text{m/s})^2}}{{2 \cdot (0.16) \cdot (9.81 , \text{m/s}^2)}} ]

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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.

- A box with an initial speed of #5 m/s# is moving up a ramp. The ramp has a kinetic friction coefficient of #5/4 # and an incline of #(3 pi )/4 #. How far along the ramp will the box go?
- How fast will an object with a mass of #15 kg# accelerate if a force of #30 N# is constantly applied to it?
- An object with a mass of #7 kg# is on a surface with a kinetic friction coefficient of # 7 #. How much force is necessary to accelerate the object horizontally at #28 m/s^2#?
- If the length of a #35 cm# spring increases to #86 cm# when a #9 kg# weight is hanging from it, what is the spring's constant?
- How are frictional forces measured?

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