Question

A man walks for some time ${}^{\prime }{t}^{\prime }$ with velocity $\left(v\right)$ due east. Then he walks for same time ${}^{\prime }{t}^{\prime }$ with velocity $\left(v\right)$ due north. The average velocity of the man is

• A. $2v$
• B. $\sqrt{2}v$
• C. $v$
• D. $\frac{v}{\sqrt{2}}$

Answer 1

The correct option is D $\frac{v}{\sqrt{2}}$

From the figure,

Displacement, $S=OB=\sqrt{(OA{)}^2+(AB{)}^2}$

$S=\sqrt{(vt{)}^2+(vt{)}^2}$

$S=\sqrt{2}vtm/s$

Total time, $T=2t$

Average velocity, $v_{avg}=\frac{S}{T}$

$v_{avg}=\frac{\sqrt{2}vt}{2t}$

$v_{avg}=\frac{v}{\sqrt{2}}m/s$

The correct option is D.