Question

A body travels the first half of the total distance with velocityV1 and the second half with velocityV2 calculate the average velocity

Answer 1

Answer:

1/V1 + 1/V2 = 2/(V avg)

Solving this, we would get the Average Velocity.

Explanation:

Velocity = Displacement /Time

Here, we take distance as displacement.

For both the velocities, distance is same. So

V1 = x / t1

V2 = x / t2

Time = Displacement / Velocity

Therefore,

t1 = x / V1

t2 = x / V2

So,

V avg = Total Displacement / Total Time

= (x + x) / t1 + t2

= 2x / (x/V1 + x/V2)

= 2x / x( 1/V1 + 1/V2 )

V avg ⇒ 2 / (1/V1 + 1/V2)

⇒ 1/V1 + 1/V2 = 2/(V avg)

Answer 2

Answer:

Average Velocity = 2V1V2/(V1+V2)

Here is the proof:

Let the total distance be x.

So time taken to cover first half =(x/2)/v1=x/(2v1)

Time taken to cover second half=(x/2)/v2=x/(2v2)

Now average velocity=Total Distance/Total time = x/((x/2v1)+(x/2v2)) = 2v1v2/v1+v2