Question

A car travels half the distance with a velocity of $20 \text{ kmh}^{-1}$ and another half distance with a velocity of $30 \text{ kmh}^{-1}$ along a straight road. The average velocity of the car in $\text{km h}^{-1}$ is

• A. 35
• B. 25
• C. 48
• D. 50
• E. 24

Hint:

Never take the simple arithmetic mean (which would be 25) for equal-distance problems. The car spends more time traveling at the slower speed, so the average velocity will always be closer to the lower speed.

Answer 1

Answer: (E)

Step 1: Understanding the Concept:
Average velocity is total displacement divided by total time. When equal distances are covered at different speeds, the average speed is the harmonic mean of the speeds.
Key Formula or Approach:
If distances are equal: $v_{avg} = \frac{2v_1v_2}{v_1 + v_2}$.

Step 2: Detailed Explanation:
Given $v_1 = 20 \text{ km/h}$ and $v_2 = 30 \text{ km/h}$.
Using the formula for average velocity over two equal distance halves:
\[ v_{avg} = \frac{2(20)(30)}{20 + 30} \]
\[ v_{avg} = \frac{1200}{50} \]
\[ v_{avg} = 24 \text{ km/h} \]

Step 3: Final Answer:
The average velocity of the car is 24 $\text{km h}^{-1}$.