Let's first find acceleration from the Newtons Second Law of Motion:
Fappl−Ffr=(mcart+mchild)a,Fappl−μk(mcart+mchild)g=(mcart+mchild)a,a=(mcart+mchild)Fappl−μk(mcart+mchild)g,a=(30 kg+9.8 s2m30 N)100 N−0.2⋅(30 kg+9.8 s2m30 N)⋅9.8 s2m=1.1 s2m.Finally, we can find the distance traveled by the cart in 3 s from the kinematic equation:
d=v0t+21at2=0+21⋅1.1 s2m⋅(3 s)2=4.95 m.Answer:
d=4.95 m.
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