Question

A body of mass m moving along a straight line covers half the distance with a speed of $2m{s}^{-1}$. The remaining half of distance is covered in two equal time intervals with a speed of $3$ $m{s}^{-1}$ and $5$ $m{s}^{-1}$ respectively. The average speed of the particle for the entire journey is?

• A. $\frac{3}{8}m{s}^{-1}$
• B. $\frac{8}{3}m{s}^{-1}$
• C. $\frac{4}{3}m{s}^{-1}$
• D. $\frac{16}{3}m{s}^{-1}$

Answer 1

The correct option is A $\frac{3}{8}m{s}^{-1}$

Let total distance be $2x$

X is traveled by 2 m/s and x/2 by 3m/s and remaining x/2 by 5 m/s.

$V_{avg.}=\frac{Totaldistance}{Totaltime}$

$V_{avg.}=\frac{2x}{\frac{x}{2}+\frac{x}{6}+\frac{x}{10}}$

$V_{avg.}=2.608m/s$