Question
The acceleration associated with a mass 'm' moving in a circular path is to be found. It is given that the velocity at any instant is v = krt, where k is a constant. Classify the motion and find acceleration.
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Answer
Given, v = krt Since velocity changes with time, the motion in circular path involves tangential acceleration. So it is a non-uniform circular motion. $\text{a}_\text{r}=\frac{\text{v}^2}{\text{r}}=\text{k}^2\text{rt}^2$ or $\text{a}_\text{k}=\frac{\text{dv}}{\text{dt}}=\text{kr}$ Net acceleration $=\text{a}_\text{n}=\sqrt{\text{a}^2_\text{r}+\text{a}^2_\text{t}}$ $=\sqrt{(\text{k}^2\text{rt}^2)^2+(\text{kr}^2)}=\text{kr}\sqrt{1+\text{k}^2\text{t}^4}.$
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