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An object of mass m has a speed v(0) as ...

An object of mass m has a speed `v_(0)` as it passes throgh the origin. Origin. It subjected to a retaeding force given by `F(x) =-Ax`. Here, A is a positive constant. Find its x-coordinate when it stops.

A

`x=v_(0)sqrt((m)/(A))`

B

`x=v_(0)sqrt((A)/(m))`

C

`x=v_(0)((m)/(A))`

D

`x=v_(0)((A)/(m))`

Text Solution

Verified by Experts

The correct Answer is:
A
`K_(f)-K_(i) =W_(F)=intFdx`
`0-1/2mv_(0)^(2) =int_(0)^(x)-Axdx`
`:. 1/2mv_(0)^(2)=(Ax^(2))`or `x=v_(0)sqrt((m)/(A))`
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