Question

The velocity vectors of a point A varies with time as $\overrightarrow{ v }=a \hat{i}+b t \hat{j},$ where $a$ and $b$ are positive constants. Find the time dependence of magnitude of velocity vector.

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

Answer 1

Answer: (C)

$V=\sqrt{V_{x}^{2}+V_{y}^{2}}=\sqrt{a^{2}+b^{2} t^{2}}$