Question

A body moving along a straight line travels one third of the total distance with a speed of $3.0\, m \,s^{-1}$. The remaining distance is covered with a speed of $4.0\, m \,s^{-1}$ for half the time and $5.0 \,m \,s^{-1}$ for the other half of the time. The average speed during the motion is

• A. $4.0\, m \,s^{-1}$
• B. $6.0\, m \,s^{-1}$
• C. $3.8\, m \,s^{-1}$
• D. $2.4\, m \,s^{-1}$

Answer 1

Answer: (C)

Let $S$ be the total distance travelled by the body. Let $t_1$ be the time taken to cover the first one third of the distance. Then
$t_{1}=\frac{S/3}{3}=\frac{S}{9}$
Let $t_2$ be the time taken for each of the remaining two journeys. Then
$S-\frac{S}{3}=4t_{2}+5t_{2}$ or $\frac{2S}{3}=9t_{2}$ or $t_{2}=\frac{2S}{27}$
Average speed $=\frac{\text{Total distance travelled}}{\text{Total time taken}}=\frac{S}{t_{1}+2t_{2}}$
$=\frac{S}{\frac{S}{9}+2\left(\frac{2S}{27}\right)}=3.8\,m\,s^{-1}$