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A particle of mass m is initially at res...

A particle of mass m is initially at rest at the origin. It is subjected to a force and starts moving along the x-axis. It kinetic energy K changes with time as `dK//dt = gamma t,` where `gamma` is a positive constant of appropriate dimensions. Which of the following statement is (are) true?

A

The force applied on the particle is constant

B

The speed of the particle is proportional to time

C

The distance of the particle from the origin increases linearly with time

D

The force is conservative

Text Solution

Verified by Experts

The correct Answer is:
A, B, D
`K=1/2mv^(2)`
`rArr (dK)/(dt) =1/2mxx2vxx(dv)/(dt)`
`rArr " " (dK)/(dt) = mv (dv)/(dt)`
Given `(dK)/(dt) = gammat`
`v dv = gamma /m t dt`
`(v^(2))/2 = gamma/m (t^(2))/2 rArr v prop t `
`(dv)/(dt) ` = constant `rArr ` F = constant
`(dx)/(dt) prop t rArr x prop t^(2)` .
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