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Solution

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Correct option is A)

$x=9t_{2}βt_{3}$.....(I)

We know that,

$v=dtdxβ$

The maximum speed is

$v=18tβ3t_{2}$

$v$ maximum, at $dtdvβ=0$

$dtdvβ=18β6t$

The time will be

$0=18β6t$

$t=3Βsec$

The position of the particle at 3 sec

Put the value of t in equation (I)

$x=9Γ9β27$

$x=81β27$

$x=54Βm$

The position of the particle will be $54Βm$.

Hence, Option A is correct

Solve any question of Motion in a Straight Line with:-

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