A particle starts from rest and performs circular motion of constant radius with speed v=α√x, where α is a constant and x is the distance covered. The correct graph of tangential acceleration aₜ and centripetal acceleration a꜀ versus time t is:
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Question

A particle starts from rest and performs circular motion of constant radius with speed v=α√x, where α is a constant and x is the distance covered. The correct graph of tangential acceleration aₜ and centripetal acceleration a꜀ versus time t is:

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G1 Physics · Accepted Answer

Given v=α√x, v²=α²x. Tangential acceleration aₜ=v(dv/dx)=α²/2, a constant. Since dx/dt=α√x, x∝t², so a꜀=v²/R∝t². The graph with constant aₜ and parabolic a꜀ is Image 4. Hence D.