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A particle moves so that x=2+27t-t^(3). ...

A particle moves so that x=2+27t-`t^(3)`. The direction of motion reverses after moving a distance of . . . Units.

A

80

B

56

C

60

D

65

Text Solution

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The correct Answer is:
B
We have, `x=2+27t-t^(3)`
`implies(dx)/(dt)=27-3t^(2)`
Since, direction will be reverse,
`therefore(dx)/(dt)=0`
`implies27-3t^(2)=0 impliest=3`
`therefore`Distance `x=2+27t-t^(3)`
`=2+27xx3-(3)^(3)`
`=2+81-27=56` units
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