Question

A particle of mass m moving in a straight line is acted upon by a force which varies its velocity as F=-kv^n. For what values of n the average velocity of the particle till it stops is one third initial velocity.

Answer 1

Answer:

The values of n = -2

Explanation:

From the above question,

They have given :

A particle of mass m moving in a straight line is acted upon by a force which varies its velocity as F=-k$v^{n}$.

Here we need to find the values of n the average velocity of the particle till it stops is one third initial velocity.

Let v₀ be the initial velocity of the particle and v₁ be the average velocity of the particle till it stops.

Given, v₁ = (1/3)v₀

Therefore,

                     v₀ + v₁ = 2v₁

                     or, v₀ = 2v₁

Now, since the force F on the particle varies as F = -kvⁿ,

therefore,

                     -kv₀ⁿ = -2kv₁ⁿ

                     or, v₀ⁿ = 2v₁ⁿ

                     or, v₀ = (2)¹/ⁿ v₁

                     or, (1/3)v₀ = (1/2)ⁿ v₁

Comparing both the equations, we get

                     (1/3)v₀ = v₁ and

                     (1/2)ⁿ v₁ = v₁

                     or, (1/2)ⁿ = 1

                      or, n = -2

Hence, the values of n = -2

For more such related questions : https://brainly.in/question/23269911

#SPJ1