Question

for a moving object, the force acting on the object varies directly with the objects acceleration. when a force of 18 n acts on a certain object, the acceleration of the object is 6 m/s². if the force is changed to 24 n, what will be the acceleration of the object?

Explanation:

Step1: Find the constant of variation

Since force \(F\) varies directly with acceleration \(a\), the equation is \(F = ka\) (where \(k\) is the constant of variation).
Given \(F = 18\) N and \(a=6\) m/s², substitute into \(F = ka\):
\(18=k\times6\)
Solve for \(k\): \(k=\frac{18}{6}=3\)

Step2: Find the new acceleration

Now \(F = 24\) N and \(k = 3\), use the equation \(F = ka\) again.
Substitute \(F = 24\) and \(k = 3\) into \(F=ka\): \(24 = 3a\)
Solve for \(a\): \(a=\frac{24}{3}=8\)

Answer:

\(8\)