Question

A particle travels half of the distance of a straight journey with a speed $6\, m / s$. The remaining part of the distance is covered with speed $2\, m / s$ for half of the time of remaining journey and with speed $4\, m / s$ for the other half of time. The average speed of the particle is

• A. 3 m / s
• B. 4 m / s
• C. 3 / 4 m / s
• D. 5 m / s

Answer 1

Answer: (B)

From $C$ to $B$ the time interval of travelling is same
So, $v_{ av }=\frac{v_{2}+v_{3}}{2}=\frac{2+4}{2}=3\, m / s$

Now, first half is covered with $6\, ms ^{-1}$ and second half with $3\, ms ^{-1}$.
So when distances are same.
$v_{ av }=\frac{2 v_{1} v_{2}}{v_{1}+v_{2}}=\frac{2 \times 6 \times 3}{6+3}=4\, ms ^{-1}$
$v_{ av }=4\, ms ^{-1}$