A) 20 m
B) 18 m
C) 16 m
D) 25 m
Correct Answer: B
Solution :
Given, \[a=\frac{dv}{dt}=6t+5\] or \[dv=(6t+5)dt\] Integrating, we get \[\int_{0}^{v}{dv}=\int_{0}^{t}{(6t+5)}dt\] or \[v=\left( \frac{6{{t}^{2}}}{2}+5t \right)\] Again \[v=\frac{ds}{dt}\] \[\therefore \] \[ds=\left( \frac{6{{t}^{2}}}{2}+5t \right)dt\] Integrating again, we get \[\int_{0}^{s}{ds}=\int_{0}^{t}{\left( \frac{6{{t}^{2}}}{2}+5t \right)}dt\] \[\therefore \] \[s=\frac{3{{t}^{3}}}{3}+\frac{5{{t}^{2}}}{2}\] when, \[t=2s,s=3\times \frac{{{2}^{3}}}{3}+\frac{5\times {{2}^{2}}}{2}\] \[=3\times \frac{8}{3}+\frac{5\times 4}{2}\] \[=8+10=18m\]
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