Question

multiple choice 1 point
suppose that a sled is accelerating at a rate of 2 m/s². if the net force is tripled and the mass is halved, then what is the new acceleration of the sled?
3 m/s²
12 m/s²
6 m/s²
2 m/s²

Explanation:

Step1: Recall Newton's second law

Newton's second law is \(F = ma\), so \(a=\frac{F}{m}\). Initially, \(a_1 = 2=\frac{F_1}{m_1}\).

Step2: Analyze the new - force and new - mass

The new force \(F_2 = 3F_1\), and the new mass \(m_2=\frac{1}{2}m_1\).

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 \(m_2=\frac{1}{2}m_1\) into the formula: \(a_2=\frac{3F_1}{\frac{1}{2}m_1}\). Since \(a_1=\frac{F_1}{m_1}=2\), then \(a_2 = 3\times2\times2\).

Answer:

\(12\ m/s^{2}\)