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A particle moves along x-axis and its displacement at any time is given by x(t) = 2t^(3) -3t^(2) + 4t in SI units. The velocity of the particle when its acceleration is zero is |
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Answer» `2.5 ms^(-1) ` Differentiating with respect to t we get `(dx)/(dt) = 6t^(2)-6t+4 or nu= 6t^(2)-6t+4 ( because(dx)/(dt)=nu)` …(i) Again differentiating with respect to t. `(d^(2)x)/(dt^(2))=12T -6` a=12t-6 `( because (d^(2)x)/(dt^(2))=a)` According to question 0=12t -6 , `t = (6)/(12)=(1)/(2)s` Putting the value of t in equation (i) we get `nu= 6xx((1)/(2))^(2)-6xx((1)/(2))+4 ` `= 6xx(1)/(4) -6xx(1)/(2)+4=(5)/(2)=2.5 ms^(-1)` |
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