# How do you determine the minimum stopping distance of a motorcycle, given its velocity and the kinetic coefficient of friction?

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A motorcycle moving at #25.0m/s# slides to a stop. Calculate the minimum stopping distance if the kinetic coefficient of friction between the tire and the road is #0.7# .

A motorcycle moving at

Minimum stopping distance = 45.49m

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To determine the minimum stopping distance of a motorcycle, you can use the equation:

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

Where:

- ( d ) is the stopping distance,
- ( v ) is the initial velocity of the motorcycle,
- ( \mu ) is the coefficient of kinetic friction between the tires and the road surface,
- ( g ) is the 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.

- If an object is moving at #4 m/s# over a surface with a kinetic friction coefficient of #u_k=80 /g#, how far will the object continue to move?
- An object with a mass of #6 kg# is on a plane with an incline of # - pi/6 #. If it takes #18 N# to start pushing the object down the plane and #1 N# to keep pushing it, what are the coefficients of static and kinetic friction?
- An object with a mass of #5 kg# is hanging from a spring with a constant of #3 (kg)/s^2#. If the spring is stretched by #6 m#, what is the net force on the object?
- An object with a mass of #8 kg# is hanging from a spring with a constant of #9 (kg)/s^2#. If the spring is stretched by # 17 m#, what is the net force on the object?
- An object with a mass of #12 kg# is on a surface with a kinetic friction coefficient of # 1 #. How much force is necessary to accelerate the object horizontally at # 14 m/s^2#?

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