A 30 kg girl and a 40 kg boy stand on rollerskates, face one another, and push off each other. If the boy accelerates backward with an acceleration of 6 m/s 2 , what will be the acceleration of the girl?

the acceleration of the girl is 8 m/s² in opposite direction.

Explanation:

Given;

mass of the girl, m₁ = 30kg

mass of the boy, m₂ = 40 kg

acceleration of the boy, a₂ = 6 m/s²

let acceleration of the girl = a₁

Apply Newton's third law of motion;

the force exerted by the girl is equal  in magnitude  to the force exerted by the boy but in opposite direction.

F₁ = -F₂

m₁a₁ = -m₂a₂

30a₁ = -(40 x 6)

30a₁ = -240

a₁ = -240 / 30

a₁ = -8 m/s² (the negative sign shows that the acceleration is in opposite direction)

Thus, the acceleration of the girl is 8 m/s² in opposite direction.