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The relation between position and time f...

The relation between position and time f for a particle , performing one dimensional motion is as under : `t = sqrt(x) +3`
Here x is in metre and t is in second .
(1) Find the displacement of the particle when its velocity becomes zero .
(2) If a constant force acts on the particle , find the work done in first 6 second .

Text Solution

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`t = sqrt(x)+3`
` :. x =(t-3)^(2)`
Now `v =(dx)/(dt) =2(t-3)`
At time t = 0 , velocity `v_(1)=-6 m//s `
At time t=6 velocity `v_(2) = 6 m//s `
` :. DeltaK = 1/2 mv_(2)^(2) - 1/2 mv_(1)^(2)`
` = 1/2 m [ (6)^(2)-(-6)^(2)] = 1/2 m [36 -36] `
` :. DeltaK = 0 " " :. "Work W = 0 "`
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