# A box with an initial speed of #7 m/s# is moving up a ramp. The ramp has a kinetic friction coefficient of #3/4 # and an incline of #pi /8 #. How far along the ramp will the box go?

The distance is

Consequently, the object's net force is

According to Newton's Second Law

So

The negative sign indicates a deceleration

We apply the equation of motion

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The distance along the ramp the box will go is approximately 9.8 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.

- A truck pulls boxes up an incline plane. The truck can exert a maximum force of #3,600 N#. If the plane's incline is #(5 pi )/12 # and the coefficient of friction is #5/12 #, what is the maximum mass that can be pulled up at one time?
- A box with an initial speed of #1 m/s# is moving up a ramp. The ramp has a kinetic friction coefficient of #5/6 # and an incline of #pi /4 #. How far along the ramp will the box go?
- How fast will an object with a mass of #4 kg# accelerate if a force of #7 N# is constantly applied to it?
- How fast will an object with a mass of #16 kg# accelerate if a force of #92 N# is constantly applied to it?
- If an object is moving at #7# #ms^-1# over a surface with a kinetic friction coefficient of #u_k=14 /g#, how far will the object continue to move?

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