Question

At an instant t, the coordinate of a particles are $ x=a{{t}^{2}},y=b{{t}^{2}} $ and $ z=0. $ The magnitude of velocity of particle at an instant t is

• A. $ t\sqrt{{{a}^{2}}+{{b}^{2}}} $
• B. $ \frac{v}{\sqrt{2}} $
• C. $ \frac{v}{\sqrt{3}} $
• D. $ 2t\sqrt{{{a}^{2}}+{{b}^{2}}} $

Answer 1

Answer: (D)

Here, displacement at an instant? Is $ s=a{{t}^{2}}\hat{i}+b{{t}^{2}}\hat{j} $ $ v=\frac{ds}{dt}=2at\hat{i}+2bt\,\hat{j} $ $ |v|=\sqrt{{{(2at)}^{2}}+{{(2bt)}^{2}}} $ $ =2t\sqrt{{{a}^{2}}+{{b}^{2}}} $