Work–Energy Theorem

Start with \(\vec F_\text{net}=m\vec a\) and connect acceleration to \(v\,dv\) along motion to get \(\Delta K\).

• Key steps overview
• Dot product with \(d\vec r\)
• Result meaning

Sum the work from all forces to find \(\Delta K\). Focus on net work, not individual forces.

• \(W_\text{net}=\Delta K\)
• Signs and energy change
• Multiple-force examples

Solve for speeds, distances, or forces without time by relating work directly to kinetic energy change.

• Find final speed
• Stopping distance
• Unknown force magnitude

Energy methods reduce vector complexity and avoid solving differential equations in many cases.

• Scalar approach
• No time needed
• Clean with varying forces

Solve mixed work–energy problems with multiple forces and changing speeds.

• Compute net work sets
• Find speed from work
• Stopping distance drills
• Variable-force (intro) problems
• Concept checks: sign & meaning

When forces are conservative, you can rewrite work in terms of potential energy and conservation laws.

• Conservative force preview
• \(W=-\Delta U\) idea
• Energy conservation setup