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A particle of mass \( m \) moves along a circular path of radius \( r \) with a centripetal acceleration \( a_{n} \) changing with time \( t \) as \( a_{n}=k t^{2} \), where \( k \) is a positive constant. The average power developed by all the forces acting on the particle during the first \( t_{0} \) seconds is
(1) \( m k r t_{0} \)
(2) \( \frac{m k r t_{0}^{2}}{2} \)
(3) \( \frac{m k r t_{0}}{2} \)
(4) \( \frac{m k r t_{0}}{4} \)
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