A) \[\frac{2{{a}_{2}}}{3}\]
B) \[-\frac{2{{a}_{2}}}{3}\]
C) \[{{a}_{2}}\]
D) Zero
Correct Answer: B
Solution :
Key Idea: Acceleration is the rate of change of velocity and velocity is the rate of change of displacement. The displacement equation is given by \[x={{a}_{0}}+\frac{{{a}_{1}}t}{2}-\frac{{{a}_{2}}{{t}^{2}}}{3}\] Velocity = rate of change of displacement i.e., \[v=\frac{dx}{dt}\] \[=\frac{d}{dx}\left( {{a}_{0}}+\frac{{{a}_{1}}t}{2}-\frac{{{a}_{2}}{{t}^{2}}}{3} \right)\] \[=0+\frac{{{a}_{1}}}{2}-\frac{2{{a}_{2}}t}{3}\] \[=\frac{{{a}_{1}}}{2}-\frac{2{{a}_{2}}t}{3}\] Acceleration = rate of change of velocity i.e., \[a=\frac{dv}{dt}\] \[=\frac{d}{dt}\left( \frac{{{a}_{1}}}{2}-\frac{2{{a}_{2}}}{3}t \right)\] \[=0-\frac{2{{a}_{2}}}{3}\] \[=-\frac{2{{a}_{2}}}{3}\]
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