Statics and Dynamics Quiz
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A 4 kg particle moves along a straight horizontal track. A friction force opposes its motion with magnitude f=6+2v Nf = 6 + 2v \text{ N}, where vv is the particle's speed in m/s (velocity-dependent friction). The particle has an initial speed of v1=8 m/sv_1 = 8 \text{ m/s} and travels a distance of 3 m.
A student attempts to apply the work–energy principle to find the final speed v2v_2 by computing friction work as Wf=−(6+2v1)(3)=−(6+16)(3)=−66 JW_f = -(6 + 2v_1)(3) = -(6+16)(3) = -66 \text{ J}, then solving 12(4)(8)2−66=12(4)v22\tfrac{1}{2}(4)(8)^2 - 66 = \tfrac{1}{2}(4)v_2^2. Which statement correctly identifies the error and its consequence?
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