Question

match the following force changes to the corresponding acceleration changes:
force options:
half the force
quadruple the force
double the force
quarter the force
acceleration results:
double the acceleration
quarter the acceleration
quadruple (4x) the acceleration
half the acceleration

Explanation:

Step1: Recall Newton's 2nd Law

Newton's second law states $a = \frac{F}{m}$, where $a$ is acceleration, $F$ is force, and $m$ (mass) is constant.

Step2: Match force change to acceleration

Analyze proportionality: $a \propto F$ (mass fixed).

• Double $F$: $a_{new}=\frac{2F}{m}=2a$
• Quarter $F$: $a_{new}=\frac{\frac{1}{4}F}{m}=\frac{1}{4}a$
• Quadruple $F$: $a_{new}=\frac{4F}{m}=4a$
• Half $F$: $a_{new}=\frac{\frac{1}{2}F}{m}=\frac{1}{2}a$

Answer:

• Double the acceleration ↔ Double the force
• Quarter the acceleration ↔ Quarter the force
• Quadruple (4x) the acceleration ↔ Quadruple the force
• Half the acceleration ↔ Half the force