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The position of a particle along the x-a...

The position of a particle along the x-axis is given by the equation, `x=t^(3)-6t^(2)+9t`, where t is measured in seconds and x in meters.
(a) Find the velocity at time t
(b) What is the velocity at t = 2 s, at = t = 4 s?
(c) What is the time instant, when particle is at rest?

Text Solution

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Strategy : Velocity `=(dx)/(dt)` i.e., change in position of particle with respect to time.
Given that , `x=t^(3)-6t^(2)+9t`
(a) `v=(dx)/(dt)=3t^(2)-12t+9`
(b) `v_(t)=2=3(2)^(2)-12(20+9=3xx4-24+9=12-24+9=21-24=-3m//s`
`v_(t)=4=3(4)^(2)-12(4)+9=3xx16-48+9=48+9=9m//s`
(c) `v_((t))=0 rArr 3t^(2)-12t+9=0 rArr 3(t^(2)-4t+3)=0 rArr 3(t-1)(t-3)=0`
This is true when t = 1 or t = 3 thus, the particle is at rest at t = 1 s and at t = 3 s.
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