Explanation
Given,
Displacement,
$$ y=k{{t}^{2}} $$
$$ \dfrac{{{d}^{2}}y}{d{{t}^{2}}}=2k $$
Since, k=1m/s2
$$ \dfrac{{{d}^{2}}y}{d{{t}^{2}}}={{a}_{y}}=2\,m/{{s}^{2}} $$
$$ {{T}_{1}}=2\pi \sqrt{\dfrac{l}{g}}.........(1) $$
$$ and $$
$$ {{T}_{2}}=2\pi \sqrt{\dfrac{l}{g+{{a}_{y}}}}.........(2) $$
Taking ratios of equation (1) and (2)
$$\dfrac{{{T}^{2}_{1}}}{{{T}^{2}_{2}}}=\dfrac{g+{{a}_{y}}}{g}=\dfrac{10+2}{10}=\dfrac{6}{5}$$
Displacement is given as$$=({ t }^{ 3 }−3{ t }^{ 2 }+2)\Longrightarrow (1)$$
We know that $$a=\dfrac { { d }^{ 2 }s }{ d{ t }^{ 2 } } $$
Differentiating (1 ) once with respect to t we get
$$\dfrac { ds }{ dt } =\dfrac { d }{ dt } ({ t }^{ 3 }−3{ t }^{ 2 }+2)=3{ t }^{ 2 }−6t$$
Differentiating once again we get
$$\dfrac { { d }^{ 2 }s }{ d{ t }^{ 2 } } =\dfrac { d }{ dt } (3{ t }^{ 2 }−6t)=6t−6$$
Given condition is $$\dfrac { { d }^{ 2 }s }{ d{ t }^{ 2 } } =6t−6=0$$
$$t=1s$$
$$s(1)=(13−3×12+2)=0m$$
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