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Displacement (x) of a particle is relate...

Displacement (x) of a particle is related to time (t) as
`x = at + b t^(2) - c t^(3)`
where a,b and c are constant of the motion. The velocity of the particle when its acceleration is zero is given by:

A

`a + (b^(2))/(3c)`

B

`a+(b^(2))/(4c)`

C

`a+(b^(2))/c`

D

`a+(b^(2))/(2c)`

Text Solution

Verified by Experts

The correct Answer is:
A
`(dx)/(dt) =a+2bt-3ct^(2)`
`(d^(2)x)/(dt^(2))=0+2b-6ct = 0 rArr t = b/(3c)`
`v = a+2b(b/(3c))-3c(b/(3c))^(2)`
`v=a +(2b^(2))/(3c) -(b^(2))/(3c) = a+(b^(2))/(3c)rArrv = a +(b^(2))/(3c)`
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