Question

A car travel half the distance with constant velocity of $40\, kmph$ and the remaining half with a constant velocity of $80\, kmph$. The average velocity of the car in $kmph$ is:

• A. $32\, km / hr$
• B. $53.3\, km / hr$
• C. $40\, km / hr$
• D. $42\, km / hr$

Answer 1

Answer: (B)

Average velocity $=\frac{\text { Total distance } / \text { displacement }}{\text { Total time }}$
Total time $= t _{1}+ t$
Now,
$t _{1}=\frac{ x }{2 \times 40} \quad, \quad t _{2}=\frac{ x }{2 \times 80}$
$\therefore $ Average velocity $=\frac{ x }{\frac{ x }{2 \times 40}+\frac{ x }{2 \times 80}}$
$=\frac{ x }{\frac{ x }{2}\left(\frac{1}{40}+\frac{1}{80}\right)}=\frac{1}{\frac{1}{80}\left(1+\frac{1}{2}\right)}$
$=\frac{80}{3 / 2}=\frac{160}{3}=53.3 km / hr$
Short Trick:
av. velocity $=\frac{2 \times V _{1} \times V _{2}}{ V _{1}+ V _{2}}$
$=\frac{2 \times 40 \times 80}{40+80}=\frac{6400}{120}$
$=53.3 km / hr$