Answer:
As, \[\text{t}=\text{A}{{\text{x}}^{\text{3}}}+\text{
B}{{\text{x}}^{\text{2}}}\]
Differentiating it w.r.t. time, we have
\[\text{1}=\left(
\text{3A}{{\text{x}}^{\text{2}}}+\text{2Bx} \right)\text{dx}/\text{dt}\]
\[\therefore \] velocity, \[\text{v}=\frac{dx}{dt}={{\left(
\text{3 A}{{\text{x}}^{\text{2}}}+\text{2Bx} \right)}^{-\text{1}}}\].......(i)
Acceleration, \[\frac{dv}{dt}=\left( -\text{1}
\right){{\left( \text{3 A}{{\text{x}}^{\text{2}}}+\text{ 2Bx}
\right)}^{-\text{2}}}\times \left( \text{6Ax }+\text{2B} \right)\frac{dx}{dt}\]
\[\therefore \]\[\frac{-(6Ax+2B)}{{{(3A{{x}^{2}}+2Bx)}^{2}}}\times
{{\left( \text{3A}{{\text{x}}^{\text{2}}}+\text{2Dx} \right)}^{-\text{1}}}\]
Retardation, =\[~-\text{a}=\frac{6Ax+2B}{{{(3A{{x}^{2}}+2Bx)}^{3}}}\]
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