A) \[t\sqrt{{{a}^{2}}+{{b}^{2}}}\]
B) \[\frac{v}{\sqrt{2}}\]
C) \[\frac{v}{\sqrt{3}}\]
D) \[2t\sqrt{{{a}^{2}}+{{b}^{2}}}\]
Correct Answer: D
Solution :
Here, displacement at an instant? Is \[s=a{{t}^{2}}\hat{i}+b{{t}^{2}}\hat{j}\] \[v=\frac{ds}{dt}=2at\hat{i}+2bt\,\hat{j}\] \[|v|=\sqrt{{{(2at)}^{2}}+{{(2bt)}^{2}}}\] \[=2t\sqrt{{{a}^{2}}+{{b}^{2}}}\]
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