# A box with an initial speed of #7 m/s# is moving up a ramp. The ramp has a kinetic friction coefficient of #1/6 # and an incline of #pi /3 #. How far along the ramp will the box go?

The distance is

Consequently, the object's net force is

Newton's Second Law of Motion states

So

A deceleration is indicated by the negative sign.

Utilize the equation of motion.

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To find the distance the box will go along the ramp, you can use the work-energy principle. The work done against friction equals the change in kinetic energy. The work done by friction is the friction force times the distance, which equals the coefficient of kinetic friction times the normal force times the distance. The normal force equals the weight of the box times the cosine of the angle of the incline. The change in kinetic energy equals the final kinetic energy minus the initial kinetic energy, which equals zero since the box eventually stops. Solving for distance gives you the answer.

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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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