A) \[4{{a}_{2}}\]
B) \[2{{a}_{2}}\]
C) \[2{{a}_{1}}\]
D) \[{{a}_{2}}\]
Correct Answer: B
Solution :
Key Idea: Acceleration is known as rate of change of velocity. The given equation is \[x={{a}_{0}}+{{a}_{1}}t+{{a}_{2}}{{t}^{2}}\] First differentiate the above equation with respect to t, to obtain velocity that is, \[v=\frac{dx}{dt}\] (velocity is rate of change of displacement) \[\therefore \] \[v=\frac{dx}{dt}={{a}_{1}}+2{{a}_{2}}t\] \[\left( \text{using}\,\frac{d}{dx}{{x}^{n}}=n\,{{x}^{n-1}} \right)\] Then second differentiation of above equation gives acceleration i.e., \[a=\frac{dy}{dt}=2{{a}_{2}}\]
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