The position of a particle as a function of time \( t \), is given by \( x(t)=a t+b t^{2}-c t^{3...

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The position of a particle as a function of time \( t \), is given by \( x(t)=a t+b t^{2}-c t^{3} \), where \( a, b \) and \( c \) are constants. When the particle attains zero acceleration, then its velocity will be
(a) \( a+\frac{b^{2}}{2 c} \)
(b) \( a+\frac{b^{2}}{4 c} \)
(c) \( a+\frac{b^{2}}{3 c} \)
(d) \( a+\frac{b^{2}}{c} \)
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