Question

How does the work required to accelerate a particle from 10 m/s to 20 m/s compare to that required to accelerate it from 20 m/s to 30 m/s ?.

Answer 1

Step-by-step explanation:

The work is equal to the change in kinetic energy:

A = Ek - Ek₀

Given:

V₁ = 10 m/s

V₂ = 20 m/s

V₃ = 20 m/s

V₄ = 30 m/s

_____________

A₃₄ / A₁₂ - ?

A₁₂ = m·V₂²/2 - m·V₁²/2 = (m/2)·(V₂² - V₁²)

A₃₄ = m·V₄²/2 - m·V₃²/2 = (m/2)·(V₄² - V₃²)

A₃₄ / A₁₂ = (V₄² - V₃²) / (V₂² - V₁²)

A₃₄ / A₁₂ = (30² - 20²) / (20² - 10²)

A₃₄ / A₁₂ = (900 - 400) / (400 - 100) = 500 / 300 ≈ 1.67

The work of A₃₄ is 1.67 times more than the work of A₁₂