using the equation: $f = m \cdot a$,
if mass (m) remains constant, which of the following describes the relationship between force (f) and acceleration (a)?

$f \propto \frac{1}{a}$
inverse

$\frac{1}{f} \propto a$
inverse

$f \propto a$
direct

Question

using the equation: $f = m \cdot a$,
if mass (m) remains constant, which of the following describes the relationship between force (f) and acceleration (a)?

$f \propto \frac{1}{a}$
inverse

$\frac{1}{f} \propto a$
inverse

$f \propto a$
direct

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Direct Variation" ], "new_concepts": [ "Newton's Second Law", "Proportionality Symbols" ], "current_concepts": [ "Direct Variation", "Newton's Second Law", "Proportionality Symbols" ] } ## Analyze the given equation and constants $$ \begin{aligned} &F = m \cdot a \ &m = \text{constant} \end{aligned} $$ ## Determine the proportionality relationship $$ \begin{aligned} &F = k \cdot a \quad (\text{where } k = m) \ &F \propto a \end{aligned} $$ ## Identify the type of relationship $$ \text{Since } F \text{ is a constant multiple of } a \text{, the relationship is direct.} $$

(A) $F \propto \frac{1}{a}$ inverse

(B) $\frac{1}{F} \propto a$ inverse

(C) $F \propto a$ direct

{ "subject": "Natural Science", "question_type": "Multiple Choice", "knowledge_point": [ "Natural Science", "Physics", "Newton's Laws of Motion" ] }

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Question

Explanation:

Analyze the given equation and constants

Determine the proportionality relationship

Identify the type of relationship

Answer: