Question

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

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

Hint:

Average Speed is not just the average of the speeds; it is Total Distance / Total Time.

Answer 1

The Correct Option is B

Step 1: First Half
Let total distance be $2S$. Time for first half ($S$): $t_1 = \frac{S}{2}$.
Step 2: Second Half
Remaining distance $S = 3t_2 + 5t_2 = 8t_2 \Rightarrow 2t_2 = \frac{S}{4}$ (total time for second half).
Step 3: Average Speed
$v_{avg} = \frac{\text{Total Distance}}{\text{Total Time}} = \frac{2S}{t_1 + 2t_2} = \frac{2S}{\frac{S}{2} + \frac{S}{4}} = \frac{2}{\frac{3}{4}} = \frac{8}{3} \text{ ms}^{-1}$.
Final Answer: (b)