Question

an object has an acceleration of 12.0 m/s/s. if the net force was tripled and the mass were doubled, then the new acceleration would be ______ m/s/s.
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new acceleration (in m/s/s)
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Explanation:

Step1: Use Newton's second law

Newton's second law is \(F = ma\), so \(a=\frac{F}{m}\). Initially, \(a_1 = 12.0=\frac{F_1}{m_1}\).

Step2: Analyze the new - force and new - mass

The new force \(F_2 = 3F_1\) and the new mass \(m_2=2m_1\).

Step3: Calculate the new acceleration

Using \(a=\frac{F}{m}\), the new acceleration \(a_2=\frac{F_2}{m_2}\). Substitute \(F_2 = 3F_1\) and \(m_2 = 2m_1\) into the formula: \(a_2=\frac{3F_1}{2m_1}\). Since \(a_1=\frac{F_1}{m_1}=12.0\), then \(a_2=\frac{3}{2}a_1\).

Step4: Find the numerical value

\(a_2=\frac{3}{2}\times12.0 = 18.0\)

Answer:

\(18.0\)