A particle starts moving rectilinearly at time t=0 such that its...

Acceleration of the particle $a=2 t-1 The$particle retards when acceleration is opposite to velocity. \Rightarrow$\text{ a } \cdot$ v<0 \Rightarrow(2 t-1)\left(t^{2}-t\right)<0 \Rightarrow t(2 t-1) $($\mathrm{t}-1)< 0$Now t is always positive \therefore(2 t-1)(t-1)<0$ or 2\mathrm{t}-$1< 0 and$\mathrm{t}-1 > 0 \Rightarrow \mathrm{t}< \frac{1}{2} and \mathrm{t} > 1$. This is not possible or$2 \mathrm{t}-1 > 0 \& \mathrm{t}-1< 0 \Rightarrow 1 / 2< \mathrm{t}< 1