The position \[x\] of a particle varies with time \[t\] as \[x=a{{t}^{2}}-b{{t}^{3}}\]. The acceleration of the particle will be zero at time \[t\] equal to [CBSE PMT 1997; BHU 1999; DPMT 2000; KCET 2000]

• A.             \[\frac{a}{b}\]
• B.             \[7.5\ km/h\]
• C.             \[\frac{a}{3b}\]          
• D.             Zero