1.

The position of particle moving along the x-axis veries with time t as `x=6t-t^(2)+4`. Find the time-interval during which the particle is moving along the positive x-direction.

Answer» `x=6t-t^(2)+4`
`v=(dx)/(dt)=6-2t=2(3-t)`
At `tlt3 s, vgt0`, the particle is moving along the positive x-direction.
At `tgt 3 s, vlt0`, the particle is moving along the negative x-direction.
At `t=3 s, v=0`.
For time-interval `t=0` to `t=3 s`, the particle is moving along the positive x-direction.


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