# If an object is moving at #7# #ms^-1# over a surface with a kinetic friction coefficient of #u_k=2/g#, how far will the object continue to move?

The distance traveled is

The mass cancels out and so does the value of 'g', and we can use the calculated acceleration and the fact that the final velocity is 0 to find the distance traveled.

Organizing:

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To find the distance (d) the object will continue to move, you can use the formula:

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

where: ( v ) = initial velocity (7 m/s) ( u_k ) = kinetic friction coefficient (( \frac{2}{g} )) ( g ) = acceleration due to gravity (approximately 9.8 m/s²)

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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.

- An object with a mass of #8 kg# is lying still on a surface and is compressing a horizontal spring by #5/4 m#. If the spring's constant is #3 (kg)/s^2#, what is the minimum value of the surface's coefficient of static friction?
- An object with a mass of #5 kg# is on a surface with a kinetic friction coefficient of # 4 #. How much force is necessary to accelerate the object horizontally at #1 m/s^2#?
- An object, previously at rest, slides #3 m# down a ramp, with an incline of #(3pi)/8 #, and then slides horizontally on the floor for another #2 m#. If the ramp and floor are made of the same material, what is the material's kinetic friction coefficient?
- Horizontal force of 50N accelerates a block of mass 3.0 kg up an incline with an A=2.0ms^-2. The angle with horizontal is 30^o. Find a) force of friction between the box and the incline b) the coefficient of kinetic friction between box and the incline?
- An object with a mass of # 18 kg# is lying on a surface and is compressing a horizontal spring by #40 cm#. If the spring's constant is # 4 (kg)/s^2#, what is the minimum value of the surface's coefficient of static friction?

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