A) \[\frac{39}{2}\]
B) \[\frac{57}{2}\]
C) \[\frac{51}{2}\]
D) \[\frac{33}{2}\]
Correct Answer: C
Solution :
\[\frac{ds}{dt}=6t-\frac{{{t}^{2}}}{6}\] Now on integrating both sides \[s=3{{t}^{2}}-\frac{{{t}^{2}}}{18}+\]constant , (where s is distance) Now put \[t=0\], then \[s=0\] gives constant equal to 0 and putting \[t=3\], we get \[s=3{{(3)}^{2}}-\frac{{{3}^{3}}}{18}=27-\frac{27}{18}=\frac{51}{2}\]. Aliter : \[\int_{0}^{s}{ds}=\int_{0}^{3}{\left( 6t-\frac{{{t}^{2}}}{6} \right)\,dt}=\frac{51}{2}\].
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