Question

for a moving object, the force acting on the object varies directly with the objects acceleration. when a force of 8 n acts on a certain object, the acceleration of the object is $2\frac{\text{m}}{\text{s}^2}$. if the acceleration of the object becomes $3\frac{\text{m}}{\text{s}^2}$, what is the force?
\boxed{\phantom{0}} n

Explanation:

Step1: Define direct variation

Since force \( F \) varies directly with acceleration \( a \), we have \( F = ka \), where \( k \) is the constant of variation.

Step2: Find the constant \( k \)

Given \( F = 8 \, \text{N} \) and \( a = 2 \, \frac{\text{m}}{\text{s}^2} \), substitute into \( F = ka \):
\( 8 = k \times 2 \)
Solve for \( k \): \( k = \frac{8}{2} = 4 \).

Step3: Calculate the new force

Now, \( a = 3 \, \frac{\text{m}}{\text{s}^2} \) and \( k = 4 \). Use \( F = ka \):
\( F = 4 \times 3 = 12 \).

Answer:

12