For a moving object, the force acting on the object varies directly with the object's acceleration. When a force of 10 N acts on a certain object, the acceleration of the object is 5 / ms2. If the acceleration of the object becomes 6 / ms2, what is the force

The force is 12 N

Step-by-step explanation:

* Lets explain how to solve the problem

- Direct variation is a relationship between two variables that can

be expressed by an equation in which one variable is equal to a

constant times the other

- If y ∝ x, then y = kx, where k is the constant of variation

* Lets solve the problem

- The force acting on the object varies directly with the object's

acceleration

∵ The force is F in newtons and a is the acceleration is m/s²

∴ F ∝ a

∴ F = ka

- To find k substitute F and a by the initial values of them

∵ A force of 10 N acts on a certain object, the acceleration of the

object is 5 m/s²

∵ F = 10 N when a = 5 m/s²

∵ F = ka

∴ 10 = k (5)

- Divide both sides by 5

∴ K = 2

- Substitute the value of k in the equation

∴ F = 2a

- Lets find the force when the acceleration is 6 m/s²

∵ a = 6 m/s²

∴ F = 2 (6) = 12

* The force is 12 N