Respuesta :
Given data:
* The mass of the object is m = 6 kg.
* The initial velocity of the object is u = 4m/s.
* The final velocity of the object is v = 3 m/s.
* The force acting on the object is F = 2 N.
Solution:
According to Newton's second law, the force acting on the object in terms of the acceleration of the object is,
[tex]F=ma[/tex]Substituting the known values,
[tex]\begin{gathered} 2=6\times a \\ a=\frac{2}{6} \\ a=0.33ms^{-2} \end{gathered}[/tex]As the acceleration is decreasing the velocity, thus, the value of acceleration is,
[tex]a=-0.33ms^{-2}[/tex]By the kinematics equation, the distance traveled by the object in terms of the acceleration, initial velocity, and final velocity is,
[tex]v^2-u^2=2aS[/tex]where S is the distance traveled by the object,
Substituting the known values,
[tex]\begin{gathered} 3^2-4^2=2\times(-0.33)\times S \\ 9-16=-0.66\times S \\ -7=-0.66\times S \\ S=\frac{-7}{-0.66} \end{gathered}[/tex]By simplifying,
[tex]\begin{gathered} S=\frac{7}{0.66} \\ S=10.6\text{ m} \end{gathered}[/tex]Thus, the distance for which force act to change the velocity from 4 m/s to 3 m/s is 10.6 meters.
