A particle which is experiencing a force, given by $\vec{F} = 3 \hat{i} - 12 \hat{j}$ , undergoes a displacement of $\vec{d} = 4 \hat{i}$ . If the particle had a kinetic energy of $3 J$ at the beginning of the displacement, what is its kinetic energy at the end of the displacement?

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Work done by the force, F → . s → = 3 i ^ + 12 j ^ ⋅ 4 i ^ = 12 J By work energy theorem, W total = ∆ K 12 J = K f - K i 12 + K i = K f ∴ K f = 12 + 3 = 15 J

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