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 :
\[x=a{{t}^{3}},y=\beta {{t}^{3}}\] \[{{v}_{x}}=\frac{dx}{dt}=3\alpha {{t}^{2}}\] \[{{v}_{y}}=\frac{dy}{dt}=3\beta {{t}^{2}}\] Resultant velocity \[v=\sqrt{v_{x}^{2}+v_{y}^{2}}\] \[=\sqrt{9{{\alpha }^{2}}{{t}^{4}}+9{{\beta }^{2}}{{t}^{4}}}\] \[=3{{t}^{2}}\sqrt{{{\alpha }^{2}}+{{\beta }^{2}}}\]
You need to login to perform this action.
You will be redirected in
3 sec
