A particle of mass \( m \) is moving along a circle of Constant radiustR. The centripetal acceleration varies as \( a=k^{2} R t^{2} \) where \( k \) is a constant and \( t \) is the time elapsed. What is the instantaneous power and average power delivered to the particle by the force acting on it.
1) \( \frac{ m }{4} k ^{2} Rt , \frac{ m }{8} k ^{2} Rt \)
2) \( \frac{ m }{2} k ^{2} Rt , \frac{ m }{4} k ^{2} Rt \)
3) \( m^{2} k^{2} R^{2} t, \frac{m}{2} k^{2} R^{2} t \)
4) \( m k^{2} R^{2} t, \frac{m}{2} k^{2} R^{2} t \)