⚡Kinetic Energy
Energy of Motion
Kinetic energy (KE) is the energy an object possesses because of its motion:
KE = ½mv²
Key features: - Always positive or zero (v² is never negative) - Depends on speed squared — doubling speed quadruples KE! - Measured in Joules (J) - A scalar quantity (no direction)
Real-world context: This is why car crashes at high speed are so much more damaging than at low speed. A car going 60 mph has 4× the KE of the same car at 30 mph.
Think About It
Two objects have the same kinetic energy but different masses. Which one is moving faster?
✏️ Worked Example
Problem: A 1500 kg car moves at 30 m/s. Find its kinetic energy. If it doubles its speed to 60 m/s, find the new KE.
📐 Key Equations
Kinetic energy
KE = (1)/(2)mv²KE ∝ v² (double speed ⇒ quadruple KE)⚠️ Common Mistakes
Misconception: Thinking that doubling speed doubles kinetic energy.
✓ Correct thinking: KE = ½mv². Speed appears squared, so doubling speed multiplies KE by 2² = 4.
Why: The v² relationship is one of the most important (and counter-intuitive) facts in physics. It explains why highway crashes are so much more severe than parking-lot fender-benders.
Misconception: Believing kinetic energy depends on the direction of motion.
✓ Correct thinking: KE = ½mv² uses speed (magnitude of velocity), not velocity. KE is a scalar — direction does not matter.
Why: A car moving north at 20 m/s and one moving south at 20 m/s have identical kinetic energies.
Misconception: Confusing kinetic energy with momentum (p = mv).
✓ Correct thinking: Momentum p = mv is linear in v; kinetic energy KE = ½mv² is quadratic in v. They are different quantities with different units (kg·m/s vs. J).
Why: Two objects can have the same momentum but very different kinetic energies (or vice versa). Choosing which quantity to use depends on the type of problem (collision vs. energy).
📝 Practice Problems
Try these problems. Check your answer when ready.
Find the kinetic energy of a 0.145 kg baseball moving at 40 m/s.
KE = (1)/(2)mv²A 1000 kg car and a 4000 kg truck are both moving at 20 m/s. Find the kinetic energy of each.
KE = (1)/(2)mv²A 2 kg object has 100 J of kinetic energy. What is its speed?
v = √((2 · KE)/(m))A 0.5 kg ball is thrown upward at 14 m/s. What is its KE at launch? At what height does its KE drop to half its initial value? (g = 10 m/s²)
KE = (1)/(2)mv², Δ KE = -mghCar A (1200 kg) moves at 30 m/s. Car B (800 kg) moves at v_B. If both have the same KE, find v_B.
(1)/(2)m_A v_A² = (1)/(2)m_B v_B²A truck's speed increases from 10 m/s to 30 m/s. By what factor does its kinetic energy increase?
An electron (m = 9.11×10⁻³¹ kg) moves at 2×10⁷ m/s. Find its kinetic energy in Joules and in electron-volts. (1 eV = 1.6×10⁻¹⁹ J)
KE = (1)/(2)mv²Finished reading through this lesson?