Question

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

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

Answer 1

Answer: (B)

Average velocity $=\frac{\text{ Total distance }/\text{ displacement }}{\text{ Total time }}$
Total time $=t_1+t$
Now,
$t_1=\frac{x}{2\times 40},t_2=\frac{x}{2\times 80}$
$\therefore$ Average velocity $=\frac{x}{\frac{x}{2\times 40}+\frac{x}{2\times 80}}$
$=\frac{x}{\frac{x}{2}\left(\frac{1}{40}+\frac{1}{80}\right)}=\frac{1}{\frac{1}{80}\left(1+\frac{1}{2}\right)}$
$=\frac{80}{3/2}=\frac{160}{3}=53.3km/hr$
Short Trick:
av. velocity $=\frac{2\times V_1\times V_2}{V_1+V_2}$
$=\frac{2\times 40\times 80}{40+80}=\frac{6400}{120}$
$=53.3km/hr$