Question

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

Explanation:

Step1: Recall Direct Variation

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

Step2: Identify the Constant

The constant of variation \( k \) is given as 32.2 feet per second squared. Substitute \( k = 32.2 \) into the direct variation formula.
So, \( F = 32.2m \).

Answer:

\( F = 32.2m \) (the second option among the given choices)