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  4. The position x of a particle varies with timer as x=at2-bt3. The acceleration of the particle will be zero at time t equal to

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Q. The position x of a particle varies with timer as $ x=a{{t}^{2}}-b{{t}^{3}}. $ The acceleration of the particle will be zero at time t equal to

CMC MedicalCMC Medical 2010

Solution:

$ x=a{{t}^{2}}-b{{t}^{3}} $ Velocity $ v=\frac{dx}{dt}=2at-3b{{t}^{2}} $ Acceleration $ a=\frac{{{d}^{2}}x}{d{{t}^{2}}}=2a-6bt $ Substituting acceleration $ a=0 $ $ \Rightarrow $ $ 2a-6bt=0 $ $ t=\frac{2a}{6b}=\frac{a}{3b} $