If an object is moving at #3 m/s# over a surface with a kinetic friction coefficient of #u_k=20 /g#, how far will the object continue to move?

Answer 1

#S=0.225 m#

#"First; let's calculate the friction force:"#
#F_f=u_k*G#
#G:"weight of object G=m.g"#
#u_k:" coefficient of friction"#

#F_f=u_k*m*g#

#F_f=20/g*m*g#

#F_f=20m#

#a=F_f/m#

#a=(20m)/m " "a=20 m/s^2 " acceleration of object"#

#"when object is stops ,the final velocity of its is zero"#

#v_f^2=v_i^2-2*a*S#

#v_f:"final velocity"#
#v_i:"initial velocity"#
#a:"acceleration"#
#"S:"displacement"#

#0=3^2-2*20*S#

#9=40*S#

#S=9/40#

#S=0.225 m#

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Answer 2

To calculate the distance the object will continue to move, we can use the equation:

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

Where:

  • (d) is the distance traveled,
  • (v) is the initial velocity of the object,
  • (\mu_k) is the coefficient of kinetic friction, and
  • (g) is the acceleration due to gravity (approximately (9.8 , \text{m/s}^2)).

Plugging in the given values:

  • (v = 3 , \text{m/s}),
  • (\mu_k = 20 , /g), and
  • (g = 9.8 , \text{m/s}^2),

We have:

[d = \frac{(3 , \text{m/s})^2}{2 \cdot (20/g) \cdot (9.8 , \text{m/s}^2)}]

[d \approx \frac{9 , \text{m}^2/\text{s}^2}{39.2 \cdot 20} , \text{m} \approx \frac{9}{784} , \text{m} \approx 0.0115 , \text{m}]

Therefore, the object will continue to move approximately (0.0115 , \text{m}).

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Answer from HIX Tutor

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.

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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