• # question_answer If the magnitude of tangential and normal accelerations of a particle moving on a curve in a plane be constant throughout, then which of the following represent the variation of radius of curvature with time? A)                B)   C)                 D)

Tangential acceleration$\frac{{{d}^{2}}}{d{{t}^{2}}}={{k}_{1}}$ (constant) $\Rightarrow$$v={{k}_{1}}t+c$ This is a equation for uniform acceleration. Normal acceleration$\frac{{{v}^{2}}}{r}={{k}_{2}}$ $\Rightarrow$$\frac{{{({{k}_{1}}t+c)}^{2}}}{r}={{k}_{2}}$ $r=\frac{{{({{k}_{1}}t+c)}^{2}}}{{{k}_{2}}}={{(\alpha t+\beta )}^{2}}$, which is parabola. [Here, r = radius is always positive]