a body travelling along a straight line travels one half of the total distance with the velocity V0.The remaining part of the distance was covered with the velocity of V1 for half of the time and with velocity V2 for other half of time. Find average velocity of the body.

Question

a body travelling along a straight line travels one half of the total distance with the velocity V0.The remaining part of the distance was covered with the velocity of V1 for half of the time and with velocity V2 for other half of time. Find average velocity of the body.

Answer 1

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Answer 2

To find the average velocity of the body, we need to calculate the total displacement and the total time taken.

Let's assume the total distance traveled by the body is D. According to the given information, the first half of the distance (D/2) is covered with velocity V0.

Using the formula for average velocity, average velocity (Vavg) is given by:

Vavg = Total displacement / Total time

Total displacement is the difference between the initial and final positions. In this case, the initial position is 0, and the final position is D/2.

So, the total displacement for the first half of the distance is D/2 - 0 = D/2.

Now, let's calculate the total time taken.

The first half of the distance is covered with velocity V0. Let's denote the time taken to cover this distance as t1.

So, we can use the formula for displacement: displacement = velocity x time

D/2 = V0 x t1

Simplifying, t1 = (D/2) / V0

For the second half of the distance, velocity V1 is used for half of the time, and velocity V2 is used for the other half of the time.

Let's denote the common time for both V1 and V2 as t2. So, each velocity is used for t2/2 time.

For velocity V1, displacement = V1 x (t2/2)

For velocity V2, displacement = V2 x (t2/2)

The total time taken is the sum of the times used for V1 and V2, which is t2/2 + t2/2 = t2.

Now, let's calculate t2 using the given information:

D/2 = V1 x (t2/2)

Simplifying, t2 = (D/V1)

D/2 = V2 x (t2/2)

Simplifying, t2 = (D/V2)

As t2 must be the same for both equations, we can equate the two expressions for t2:

(D/V1) = (D/V2)

Cross multiplying, V1 = V2

Now, we can calculate the total time taken:

Total time = t1 + t2 = (D/2) / V0 + (D / V1)

Finally, we can calculate the average velocity:

Vavg = Total displacement / Total time = (D/2) / Total time

Substituting the values we found earlier:

Vavg = (D/2) / ((D/2) / V0 + (D / V1))

Simplifying further:

Vavg = (D/2) / ((D/V0) + (D/V1))

Vavg = 2 / (1/V0 + 1/V1)

So, the average velocity of the body is given by the formula 2 / (1/V0 + 1/V1).