A) \[3t\sqrt{{{\alpha }^{2}}+{{\beta }^{2}}}\]
B) \[3{{t}^{2}}\sqrt{{{\alpha }^{2}}+{{\beta }^{2}}}\]
C) \[{{t}^{2}}\sqrt{{{\alpha }^{2}}+{{\beta }^{2}}}\]
D) \[\sqrt{{{\alpha }^{2}}+{{\beta }^{2}}}\]
Correct Answer: B
Solution :
Given \[\operatorname{x}=\alpha {{t}^{3}},\,\,y=\beta {{t}^{3}}\] \[{{v}_{x}}=\frac{dx}{dt}=3\,\alpha {{t}^{2}}\] \[{{v}_{y}}=\frac{dy}{dt}=3\,\beta {{t}^{2}}\] \[{{\operatorname{v}}_{R}} =Resultant velocity\] \[=\,\,\,\sqrt{v_{x}^{2}+v_{y}^{2}}\,\,=\,\,3{{t}^{2}}\sqrt{{{\alpha }^{2}}+{{\beta }^{2}}}\]
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