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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 alphav^(3)`

B

`2betav`

C

`2alpha betav^(3)`

D

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

Text Solution

Verified by Experts

The correct Answer is:
A
`t=alphax^(2)+betax`
`(dt)/(dx)=2alphax+betaimpliesv=1/((2alphax+beta))`
`v=(2alphax+beta)^(-1)`
`(dv)/(dx)=(-1)(2alphax+beta)^(-2)(2alpha)`
`=-(2alpha)/((2alphax+beta)^(2))=-2alphav^(2)`
`a=v(dv)/(dt)=-2alphav^(3)`
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