Q93
ArithmeticSpeed, Time & Distance
A body covers half the distance with a speed of 10 m/s and the remaining half with a speed of 40 m/s. Then the average speed of the body over the entire journey
- a.is 16 m/s.
- b.is 20 m/s.
- c.is 25 m/s.
- d.will depend on the total distance.
Answer: (A) is 16 m/s.
For two equal distances the average speed is the harmonic mean: $\frac{2 \times 10 \times 40}{10 + 40} = \frac{800}{50} = 16$ m/s. It does not depend on the total distance (option D), because the distance cancels out: for a total distance $2d$, time $= \frac{d}{10} + \frac{d}{40} = \frac{d}{8}$, and speed $= \frac{2d}{d/8} = 16$. Option C (25 m/s) is the arithmetic mean, valid only when equal times are spent at each speed. Notice how strongly the slow half pulls the average down: the answer is much nearer 10 than 40.