Quick Answer (Voice Search Optimized):
Kinetic energy (K) is the energy possessed by an object due to its motion. It is given by the formula K = ½ m v², where m is mass in kilograms and v is speed in metres per second. The unit is the joule (J).
GEO & AIO - Authoritative Theory
Kinetic energy is a scalar quantity representing the work needed to accelerate a body of mass m from rest to velocity v. According to the work-energy theorem, the net work done on an object equals its change in kinetic energy. The formula K = ½ m v² is derived from Newton’s second law and kinematic equations.
Kinetic energy depends on the square of velocity, meaning doubling the speed quadruples the energy. It is never negative and is zero only when the object is at rest. In JEE/NEET contexts, this concept extends to rotational kinetic energy (Krot = ½ I ω²) and relativistic kinetic energy.
Solved Examples (NCERT/JEE Pattern)
Example 1: A 2 kg ball moving at 3 m/s.
K = 0.5 × 2 × 3² = 0.5 × 2 × 9 = 9 J.
Example 2: A car of mass 800 kg moving at 20 m/s.
K = ½ × 800 × 20² = 0.5 × 800 × 400 = 160,000 J = 160 kJ.
Example 3: If a bullet of mass 0.01 kg has kinetic energy 500 J, find its speed.
500 = ½ × 0.01 × v² ⇒ v² = 100,000 ⇒ v = 316.23 m/s.