A) \[V=2i+2t\,\hat{j}\]
B) \[V=2t\,\,\hat{i}+2t\,\hat{j}\]
C) \[V=t\,\,\hat{i}+{{t}^{2}}\,\hat{j}\]
D) \[V=2\,\,\hat{i}+{{t}^{2}}\,\hat{j}\]
Correct Answer: A
Solution :
Given \[r=2t\,\hat{i}+{{t}^{2\,}}\hat{j}\] Velocity vector \[v=\frac{dr}{dt}\] and using \[\frac{d}{dx}{{x}^{n}}=n{{x}^{n-1}}\] We have, \[\frac{dr}{dt}=2\,\hat{i}+2t\,\hat{j}\]
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