Question
The power supplied by a force acting on a particle moving in a straight line is constant . The velocity of the particle varies with the displacement `x` as
Answer: Option D
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(D) `because ` p = Fv = (ma) v = `m((d^2 x)/(dt^2)) ((dx)/(dt))`
Since , power is constant ,
`:.` ` ((d^2 x)/(dt^2)) ((dx)/(dt))` = k
or `((d)/(dt)) ((dx)/(dt))^2 = k`
or `((dx)/(dt))^2 = k_1` t
or ` (dx)/(dt) = sqrt(k_1 t) = k _2 t^(1/2)`
or ` x = k_3 t^(3/2)`
Hence `(dx)/(dt) prop t^(1/2) prop x^(1/3)`
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