A) \[{{\operatorname{f}}_{o}}T\]
B) \[{{\operatorname{f}}_{o}}{{T}^{2}}\]
C) \[{{\operatorname{f}}_{o}}^{2}{{T}^{2}}\]
D) \[\frac{{{\operatorname{f}}_{o}}T}{2}\]
Correct Answer: D
Solution :
\[\operatorname{f}={{f}_{o}}-\frac{{{f}_{o}}t}{T}\] \[\operatorname{f}=\frac{dv}{dt}={{f}_{o}}-\frac{{{f}_{o}}t}{T}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\left[ \operatorname{a}=f=\frac{dv}{dt} \right]\] \[dv={{f}_{o}}\operatorname{dt}-\frac{{{f}_{o}}t}{T}\] Integrating both sides \[\operatorname{v}={{f}_{o}}t-\frac{{{f}_{o}}{{t}^{2}}}{T\times 2};t=0,\,\,v=0\] \[{{f}_{o}}-\frac{{{f}_{o}}t}{T}=0,t=T\] \[\operatorname{v} at t = T\] \[\operatorname{v}={{f}_{o}}T-\frac{{{f}_{o}}{{T}^{2}}}{2T}\] \[\operatorname{v}=\frac{{{f}_{o}}\operatorname{T}}{2}\]You need to login to perform this action.
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