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 :
[b] \[x=\,\propto \,{{t}^{3}}y=\beta {{t}^{3}}\] \[{{v}_{x}}=3\,\propto \,{{t}^{3}}{{v}_{y}}=3\beta {{t}^{2}}\] \[={{\left( 3a{{t}^{2}} \right)}^{2}}+{{\left( 3\beta {{t}^{2}} \right)}^{2}}\] \[=9{{\alpha }^{2}}{{t}^{4}}+9{{\beta }^{2}}{{t}^{4}}\] \[V=\sqrt{9{{t}^{4}}\left[ {{\alpha }^{2}}+{{\beta }^{2}} \right]}\] \[V=3{{t}^{2}}\sqrt{{{\alpha }^{2}}+{{\beta }^{2}}}\]
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