1.

The velocity of particle at time t is given by the relation `v=6t-(t^(2))/(6)`. The distance traveled in 3 s is, if s=0 at t=0A. `(39)/(2)`B. `(57)/(2)`C. `(51)/(2)`D. `(33)/(2)`

Answer» Correct Answer - C
Given `v=(ds)/(dt)=6t-(t^(2))/(6)`
On intergrating both side, we get
`s=3t^(2)-(t^(3))/(18)+` constant Now, put at t=0 , we get
constant =0
`:. S=3t^(2)-(t^(3))/(18)`
Now, distance traveled in `3s=3(3)^(2)-((3)^(3))/(18)`
`=27-(27)/(18)=(51)/(2)`


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