Physics - Circular Motion Question with Solution | TestHub

$\vec{v}=2t\hat{i}+t^2\hat{j}$, $\vec{a}=2\hat{i}+2t\hat{j}$; at $t=1$: $a=\sqrt{8}$ m/s${}^2$ - (A) wrong.

$V=\sqrt{4t^2+t^4}$; $a_t=\frac{dV}{dt}=\frac{8t+4t^3}{2\sqrt{4t^2+t^4}}$; at $t=1$: $a_t=\frac{6}{\sqrt{5}}$ m/s${}^2$ - (B), (C) wrong.

$a_c=\sqrt{a^2-a_t^2}=\sqrt{8-\frac{36}{5}}=\frac{2}{\sqrt{5}}$ m/s${}^2$.

$R=\frac{V^2}{a_c}=\frac{5}{2/\sqrt{5}}=\frac{5\sqrt{5}}{2}$ m - (D)