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The relation between time t and displace...

The relation between time t and displacement x is `t = alpha x^2 + beta x,` where `alpha and beta` are constants. The retardation is

A

`2 alpha v^(3)`

B

` 2 beta v^(3) `

C

` 2alpha betav ^(3) `

D

` 2 beta ^(2) v^(3) `

Text Solution

Verified by Experts

The correct Answer is:
A
` (dt)/( dx) =2alpha x+beta rArr v = (1)/( 2alpha x+beta ) " "because " "a=( dv)/(dt) =(dv)/(dx) .(dx)/(dt) `
` a=v (dv)/(dx) =( -v.2alpha )/((2alpha x +beta)^(2)) =-2alpha v.v^(2) =-2alpha v^(3) " "therefore " " ` Retardation =`2alpha v^(3)`
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