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