Question

If a body travels half of the total distance with velocity of \(20 \, \text{km/hr}\) and other half with velocity of \(30 \, \text{km/hr}\), find average velocity.

Hint:

Remember: When the object travels equal distances at different speeds, the average velocity is calculated by using the total time and total distance.

Answer 1

Step 1: Use the formula for average velocity.
The average velocity is given by the formula: \[ \text{Average velocity} = \frac{\text{Total distance}}{\text{Total time}} \]
Step 2: Calculate the total distance.
Let the total distance be \( D \). The body travels half the distance with velocity \( 20 \, \text{km/hr} \) and the other half with velocity \( 30 \, \text{km/hr} \).
Step 3: Calculate the time taken for each half.
For the first half of the distance, the time taken is: \[ t_1 = \frac{\frac{D}{2}}{20} = \frac{D}{40} \] For the second half of the distance, the time taken is: \[ t_2 = \frac{\frac{D}{2}}{30} = \frac{D}{60} \]
Step 4: Calculate the total time.
The total time is the sum of \( t_1 \) and \( t_2 \): \[ \text{Total time} = t_1 + t_2 = \frac{D}{40} + \frac{D}{60} \] \[ \text{Total time} = \frac{3D}{120} + \frac{2D}{120} = \frac{5D}{120} = \frac{D}{24} \]
Step 5: Calculate the average velocity.
Now, use the formula for average velocity: \[ \text{Average velocity} = \frac{D}{\frac{D}{24}} = 24 \, \text{km/hr} \] Thus, the average velocity is: \[ \boxed{24 \, \text{km/hr}} \]