Kinetic Energy Calculator

Physics • K = ½ m v² • Step-by-Step

kg m/s

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.

Frequently Asked Questions (FAQs)

Q1: What is kinetic energy in simple words?
Kinetic energy is the energy an object has because it is moving. The faster and heavier it is, the more kinetic energy it has.
Q2: What is the SI unit of kinetic energy?
The SI unit is joule (J). 1 J = 1 kg · m² / s².
Q3: Can kinetic energy be negative?
No, kinetic energy is always non-negative because mass and velocity squared are both non-negative. It is zero only at rest.
Q4: How is kinetic energy related to momentum?
K = p² / (2m), where p = mv is momentum. This form is useful in collision problems.
Q5: What happens to kinetic energy when velocity is doubled?
Kinetic energy quadruples because it is proportional to the square of velocity.