Physics - Kinematics Question with Solution | TestHub

Acceleration of the particle $a=2t-1$ The particle retards when acceleration is opposite to velocity. $$\Rightarrow \text{ a }\cdot v<0\Rightarrow (2t-1)\left(t^2-t\right)<0\Rightarrow t(2t-1)$$ $(\mathrm{t}-1)<0$ Now t is always positive $$\therefore (2t-1)(t-1)<0$$ 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 $2\mathrm{t}-1>0\&\mathrm{t}-1<0\Rightarrow 1/2<\mathrm{t}<1$