Question

if you need four times the acceleration to move a 2,000 kg suv compared to a 500 kg sports car with the same force, what is the relationship between mass and acceleration?
acceleration and mass are unrelated
acceleration increases as mass increases
acceleration is not affected by mass
acceleration decreases as mass increases

Explanation:

Step1: Apply Newton's second law

Newton's second law is \(F = ma\), where \(F\) is force, \(m\) is mass, and \(a\) is acceleration. Let \(F\) be the same for both vehicles. For the SUV, \(F = m_1a_1\) (\(m_1 = 2000\space kg\)), and for the sports - car, \(F=m_2a_2\) (\(m_2 = 500\space kg\)). Since \(F\) is the same, \(m_1a_1=m_2a_2\). We know \(a_1 = 4a_2\). Substitute \(a_1\) into the equation: \(2000\times4a_2=500\times a_2\) (not necessary for the relationship, just to show the substitution concept). From \(F = ma\), we can express \(a=\frac{F}{m}\). When \(F\) is constant.

Step2: Analyze the relationship

If \(F\) is constant (same force), \(a\propto\frac{1}{m}\) (inverse - proportionality). As \(m\) increases, \(a\) decreases. For example, if \(m\) doubles (\(m_2 = 2m_1\)), then \(a_2=\frac{F}{2m_1}=\frac{1}{2}a_1\) (where \(a_1=\frac{F}{m_1}\)).

Answer:

Acceleration decreases as mass increases