Sarah's acceleration is [tex]-0.49 m/s^2[/tex]
Explanation:
The force of kinetic friction acting on Sarah has a magnitude which is given by:
[tex]F_f = \mu mg[/tex]
where
[tex]\mu[/tex] is the coefficient of kinetic friction
m is Sarah's mass
g is the acceleration of gravity
Moreover, according to Newton's second law of motion, we know that the net force on Sarah is equal to its mass times its acceleration:
[tex]F=ma[/tex]
where a is the acceleration
Since the force of friction is the only force acting on Sarah, we can say that the net force is equal to the force of friction, therefore:
[tex]F=-\mu mg = ma[/tex]
where the negative sign is due to the fact that the force of friction has a direction opposite to the motion of Sarah. Solving for a, we find
[tex]a=-\mu g[/tex]
And substituting the following values:
[tex]\mu = 0.05[/tex] (coefficient of friction)
[tex]g=9.81 m/s^2[/tex] (acceleration of gravity)
we find:
[tex]a=-(0.05)(9.81)=-0.49 m/s^2[/tex]
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