A body cover first 1/3 part of a journey with a velocity of 2m/s next 1/3 with a velocity of 3m/s and rest of a journey with a velocitu 6m/s the average velocity of the body will be ?

Question

Answer

Calculation of Average Velocity of a Body

Given Data

Initial Velocity (u) = 0 m/s

Velocity in the first 1/3 part of the journey (v1) = 2 m/s

Velocity in the next 1/3 part of the journey (v2) = 3 m/s

Velocity in the rest of the journey (v3) = 6 m/s

Total distance travelled (s) = 1 unit (assumed)

Calculation

The average velocity of the body during the entire journey can be calculated using the formula:

average velocity = total displacement / total time

As the total distance travelled is 1 unit and the body travels 1/3rd of the distance with a velocity of 2 m/s, next 1/3rd of the distance with a velocity of 3 m/s and the remaining 1/3rd with a velocity of 6 m/s, we can calculate the total displacement of the body as follows:

total displacement = (1/3)*1 + (1/3)*1 + (1/3)*1 = 1

Now, we need to calculate the time taken by the body to travel the entire distance. As the distance travelled and the velocity of the body is not constant throughout the journey, we cannot use the formula for uniform motion. Instead, we need to calculate the time taken for each part of the journey separately and add them to get the total time taken by the body. Here's how we can do it:

Time taken to travel the first 1/3rd of the distance = distance / velocity = (1/3)*1 / 2 = 1/6 s

Time taken to travel the next 1/3rd of the distance = distance / velocity = (1/3)*1 / 3 = 1/9 s

Time taken to travel the remaining 1/3rd of the distance = distance / velocity = (1/3)*1 / 6 = 1/18 s

Total time taken by the body to travel the entire distance = (1/6) + (1/9) + (1/18) = 7/18 s

Now, we can calculate the average velocity of the body during the entire journey as:

average velocity = total displacement / total time = 1 / (7/18) = 18/7 m/s = 2.57 m/s (approx)

Conclusion

Therefore, the average velocity of the body during the entire journey is 2.57 m/s (approx).

Answer

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