Physics, asked by zakir7581p0visq, 1 year ago

a particle moving in a straight line moves half a distance with a constant velocity of 10m/s and next half distance with a constant velocity of 5m/s . What is average velocity of particle during the entire motion?

Answers

Answered by Anonymous
18

Let the total distance travelled by the particle be 2 x .

The particle covers half of the distance with constant velocity of 10 m/s and the other half of the distance with constant velocity of 5 m/s .

Half of the distance travelled by the particle will be half of 2 x .

⇒ 1/2 of 2 x ⇒ 1/2 × 2 x ⇒ x

∴ The particle covers x distance with 10 m/s and the remaining x distance with 5 m/s .

Let the total time taken by the particle to cover 2 x distance be T .

The average velocity of the body is the total displacement in unit total time .

Average velocity = 2 x / T .

Let the time taken to cover x with 10 m/s be t₁ and the time taken to cover x with 15 m/s be t₂ .

T = t₁ + t₂

We know that : velocity = displacement / time

Time = displacement / velocity .

For the average velocity :

⇒ Time T = 2 x / v

⇒ Time T = 2 x / v m/s

For the first case

Velocity = 10 m/s

Time = t₁

Displacement = x

Time t₁ = x / 10 m/s

For the second case

Velocity = 5 m/s

Time = t₂

Displacement = x .

Time t₂ = x / 5 m/s

Average velocity

From the above we can write :

T = t₁ + t₂

⇒ 2 x / v m/s = x / 5 m/s + x / 10 m/s

⇒ 2 x / v m/s = x / m/s ( 1 / 5 + 1 / 10 )

⇒ 2 / v =  ( 1 / 5 + 1 / 10 )

⇒ 2 / v = 1 / 5 + 1 / 10

⇒ 2 / v = ( 2 + 1 ) / 10

⇒ 2 / v = 3 / 10

⇒ v = 20 / 3

⇒ v = 6.666 m/s

The average velocity is 6.67 m/s .

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