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A point P moves in counter-clockwise dir...

A point P moves in counter-clockwise direction on a circular path as shown in the figure. The movement of 'P ' is such that it sweeps out a length ` s = t ^ 3 + 5` where s is in meters and t is in seconds. The radius of the path is 20 m. The acceleration of ' P ' when t = 2 s is nearly:

A

` 14 m // s^(2)`

B

` 13 m // s^(2)`

C

` 12 m //s^(2)`

D

` 7 2 m//s^(2)`

Text Solution

Verified by Experts

The correct Answer is:
A
`s = t ^(3) + 5 , R = 20 m`
` v = ( ds)/( dt) = 3 t^(2) rArr v |_(t= 2) = 12 m//s `
`a_(t) = ( dv)/( dt) = 6 t rArr a_(t) |_(t = 2) = 12 m//s ^(2)`
`a_(R) = (v^(2))/(R) = (144)/( 20) = 7.2 m// s^(2)`
`a = sqrt( a_(t)^(2) + a_(R)^(2)) = sqrt((7.2)^(2) + (12) ^(2)) = 14 m// s^(2)`
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