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Suppose a particle is moving with tangential acceleration of constant magnitude but with centripetal acceleration magnitude variable with time (suppose proportional to $\,t^2$). Then what does the path of the motion look like?

Also please tell can the same situation is possible if we have to keep the radius constant ?

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    $\begingroup$ Please note that homework-like questions and check-my-work questions are generally considered off-topic here. We intend our questions to be potentially useful to a broader set of users than just the one asking, and prefer conceptual questions over those just asking for a specific computation. $\endgroup$ Aug 6 at 6:50

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