A particle of mass n is moving in a circular path of constant radius r such that its centripetal acceleration \(\alpha_c\) is varying with time t as, a_c = k^2 r t , The power delivered to the particle by the forces acting on it is
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Here the tangential acceleration also exits which requires power.
Given that a_c = k r t^2 and \(a_{c} = \frac{v^{2}}{r}\) ∴ ∴ \(\frac{v^{2}}{r} = k^{2} r t\)
or v^{2} = k^{2} r^{2} + t^{2} or v = k r t
Tangential acceleration \(a = \frac{dv}{dt} = kr\)
Now force \(F = m \times a = mkr\)
So power \(P = F \times v = mkr \times krt = mk^{2}r^{2}t\)
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