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The position of a particle moving along ...

The position of a particle moving along x-axis varies eith time t as `x=4t-t^(2)+1`. Find the time interval(s) during which the particle is moving along positive x-direction.

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If the particle moves along positive x-direction, its x-coordinate must increase with time t.
x-coordinate will increase with time t if `(dx)/(dt) gt 0`.
`(dx)/(dt)=4 -2t`
`(dx)/(dt) gt 0rArr 4-2t gt 0rArr t lt 2`
Hence, the particle moves in positive x-direction during time-interval `0 lt t lt 2`.
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