Let's first find the acceleration of the object from the Newton's Second Law of Motion (we assume that when object reaches the velocity of 20 m/s at the foot of the plane, it releases and the only force of friction acts on it):
−Fk.fr.=ma,−μkmg=ma,a=−μkg=−0.25⋅9.8 s2m=−2.45 s2m.The sign minus means that the object decelerates.
Then, we can find the distance traveled by the object until it finally stops:
v2=v02+2ad,d=2a−v02=2⋅(−2.45 s2m)−(20 sm)2=81.6 m.Answer:
d=81.6 m.
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