question_answer

A body of mass 0.5 kg is moving with a constant velocity of 2 m/s. In order to bring it to rest in a distance of 2m, find the work done.

Answer:

Given,   \[m=0.5kgu=2m/s\]                 \[v=0m/sS=2m\]                 \[W=?\] We know, \[W=F\times S\] and \[F=ma\] From the relation, \[{{v}^{2}}-{{u}^{2}}=2aS\] \[\Rightarrow a=\frac{{{V}^{2}}-{{u}^{2}}}{2S}\] \[\therefore F=m\left( \frac{{{V}^{2}}-{{u}^{2}}}{2S} \right)\] \[\therefore W=m\left( \frac{{{V}^{2}}-{{u}^{2}}}{2S} \right)\times S=\frac{m}{2}({{v}^{2}}-{{u}^{2}})\] \[=\frac{0.5}{2}({{0}^{2}}-{{2}^{2}})\] \[=\frac{1}{2}\times 0.5\times -4=-1J\]