Sarah's acceleration is ![-0.49 m/s^2](https://tex.z-dn.net/?f=-0.49%20m%2Fs%5E2)
Explanation:
The force of kinetic friction acting on Sarah has a magnitude which is given by:
![F_f = \mu mg](https://tex.z-dn.net/?f=F_f%20%3D%20%5Cmu%20mg)
where
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:
![F=ma](https://tex.z-dn.net/?f=F%3Dma)
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:
![F=-\mu mg = ma](https://tex.z-dn.net/?f=F%3D-%5Cmu%20mg%20%3D%20ma)
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
![a=-\mu g](https://tex.z-dn.net/?f=a%3D-%5Cmu%20g)
And substituting the following values:
(coefficient of friction)
(acceleration of gravity)
we find:
![a=-(0.05)(9.81)=-0.49 m/s^2](https://tex.z-dn.net/?f=a%3D-%280.05%29%289.81%29%3D-0.49%20m%2Fs%5E2)
Learn more about acceleration and forces:
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