A) \[2t(a+b)\]
B) \[2t\sqrt{{{a}^{2}}+{{b}^{2}}}\]
C) \[2t\left( \sqrt{{{a}^{2}}-{{b}^{2}}} \right)-2t\left( \sqrt{{{a}^{2}}-{{b}^{2}}} \right)\]
D) \[\sqrt{{{a}^{2}}+{{b}^{2}}}\]
Correct Answer: B
Solution :
\[r=\hat{i}x+\hat{j}y\] \[=\hat{i}a{{t}^{2}}+\hat{j}b{{t}^{2}}\] \[v=\frac{dr}{dt}=\hat{i}2at+\hat{j}2bt\] Magnitude of \[\vec{v}=\sqrt{4{{a}^{2}}{{t}^{2}}+4{{b}^{2}}{{t}^{2}}}\] \[=2t\sqrt{{{a}^{2}}+{{b}^{2}}}\]
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