Question

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

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

Answer 1

Answer: (A)

Let the total distance travelled by the body is $2 S$. If $t_{1}$ is the time taken by the body to travel first half of the distance, then
$t_{1}=\frac{s}{2}$
Let $t_{2}$ be the time taken by the body for each time interval for the remaining half journey.
$\therefore \,\,\,\,S=3 t_{2}+5 t_{2}=8 t_{2}$
So, average speed $=\frac{\text { Total distance travelled }}{\text { Total time taken }} $
$=\frac{2 S}{t_{1}+2 t_{2}} $
$=\frac{2 S}{\frac{S}{2}+\frac{S}{4}} $
$=\frac{8}{3} \,ms ^{-1}$