If the velocity of a particle is reduced to half of its initial value , then the kinetic energy of the particle will

The correct answer is reduce to one-fourth of its original value.

Important Points

• Kinetic Energy=  \(1 \over 2 \)\(mv^2\) (m is the mass of the body and v is the velocity at which the body is moving)
• So, when the velocity is reduced by half so the equation becomes
• Kinetic Energy = \(1 \over 2 \)\(mv^2\) = \({1\over 2} m \left( \frac {v}{2}\right)^2\) = \({1\over 2} m {v^2\over 4}\)  = \({1\over 4} \left({1\over 2} mv^2\right)\)
• From the above equation, we can see the kinetic energy is one-fourth the original value.

Key Points

• Kinetic Energy is the energy possessed by a body by the virtue of its motion.
• If a body is moving in a horizontal circle then its kinetic energy is the same at all points, but if it moving in a vertical circle, then the kinetic energy is different at different points.
• Example: A bullet fired from a gun can pierce a target due to its kinetic energy.

Additional Information

• The energy of an object is its capacity for doing work.
• Types of energy
  • Mechanical energy
  • Heat energy
  • Sound energy
  • Light energy
  • Chemical energy 
• Mechanical energy is of two types: Kinetic energy and Potential energy.
• Potential energy is the energy possessed by a body by virtue of its position.