Question

e force of gravity on an object varies directly with its mass. the constant of variation due to gravity is 32.2 feet per cond squared. which equation represents f, the force on an object due to gravity according to m, the objects mass?
$f = \frac{32.2}{m^{2}}$
$f = 32.2m$
$f = \frac{16.1}{m^{2}}$
$f = 16.1m$

Explanation:

Step1: Recall direct variation formula

The formula for direct variation is \(y = kx\), where \(k\) is the constant of variation. Here, \(F\) (force) varies directly with \(m\) (mass), so \(F=km\).

Step2: Identify the constant of variation

Given that the constant of variation \(k = 32.2\) (feet per second squared). Substituting \(k = 32.2\) into \(F = km\), we get \(F=32.2m\).

Answer:

\(F = 32.2m\) (the second option)