3. Newton's Second Law: \(F = ma\)

Newton's Second Law connects force, mass, and acceleration:
\[ F = m \times a. \]

For the same mass, more force means more acceleration. For the same force, more mass means less acceleration.

Worked example: a \(5\text{ kg}\) cart pushed by \(20\text{ N}\) accelerates at \(a = F/m = 20/5 = 4\text{ m/s}^2\).

Deep explanation. Newton's Second Law connects force, mass, and acceleration: \(F = ma\). More net force causes more acceleration when mass is constant. More mass causes less acceleration when the same net force is applied.

The units also tell the story. Force is measured in newtons. One newton is the force needed to accelerate \(1\text{ kg}\) at \(1\text{ m/s}^2\). If the problem gives force and mass, divide to find acceleration. If it gives mass and acceleration, multiply to find force.

Worked examples. A \(6\text{ kg}\) object pushed by \(18\text{ N}\) accelerates at \(18/6 = 3\text{ m/s}^2\). A \(2\text{ kg}\) object accelerating at \(5\text{ m/s}^2\) has net force \(2 \times 5 = 10\text{ N}\).

⚠️ Common misconception: students often multiply when they should divide to find acceleration.

💡 Tip: \(a = F/m\).