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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^(2)`
`implies (dx)/(dt) = 27 - 3t^(2)`
since, direaction will be reverse,
`:. (dx)/(dt) = 0`
`implies 27 - 3t^(2) = 0`
`implies t = 3`
`:.` Distance `x 2 + 27t - t^(3)`
`= 2 + 27 xx 3 - (3)^(3)`
`= 2 + 81 - 27 = 56` units
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