A) \[{{f}_{o}}t\]
B) \[\frac{1}{2}{{f}_{o}}{{T}^{2}}\]
C) \[{{f}_{o}}{{T}^{2}}\]
D) \[\frac{1}{2}{{f}_{o}}T\]
Correct Answer: D
Solution :
\[f=\frac{dv}{dt}={{f}_{0}}\left( 1-\frac{t}{T} \right)\] At\[t=0,f={{f}_{0}}\]at\[T={{T}_{0}},f=0\] We have to calculate the velocity of the particle in the time from\[t=0\]to\[t=T\]sec \[\frac{dv}{dt}={{f}_{0}}\left( 1-\frac{t}{T} \right)\] \[\int{dv}=\int_{0}^{T}{{{f}_{0}}\left( 1-\frac{t}{T} \right)}dt\] \[v={{f}_{0}}\left( t-\frac{{{t}^{2}}}{2T} \right)_{0}^{T}\] \[={{f}_{0}}\left[ T-\frac{{{T}^{2}}}{2T} \right]\] \[v={{f}_{0}}\left[ T-\frac{T}{2} \right]\] Velocity, \[v={{f}_{0}}\left( \frac{T}{2} \right)\]
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