# Kinetic Energy: Its Relation with Movement and Velocity

Kinetic Energy and Movement (Velocity).- To obtain the relation between energy and movement, let's imagine a particle of mass m moving in a straight line with initial velocity Vi . A net constant force F is then applied parallel to its movement, over a distance d. Then, the work done over the particle is W = Fd. As F = ma (a, acceleration) and using the kinetic energy formula Vf2 = Vi2 + 2ad, where Vf is the final velocity, we get:

W = Fd = mad = m[(Vf2 - Vi2) / 2d]d

That is, W = ½mVf2 - ½mVi2

It is clear we have a difference between final and initial quantities.

The kinetic energy (translational energy) of a particle is defined by physicists as the quantity ½mv2 .

Ec = ½mv2.

W can also be written

W = Ec

That is, the net work done on an object is equal to the change in his kinetic energy. This result is known as the work-kinetic energy theorem.

Let's notice W is the net work done over the object.

Example. Starting from rest, you push your 1.000 kg car over a 5 meters distance, on an horizontal ground, applying an also horizontal 400 N force. What is the car kinetic energy change?; What is its final velocity at the end of the 5 meters displacement? Disregard any friction force.

Solution. The change in kinetic energy must be equal to the net work done on the car,
W = Fd
= (400 N)(5 m) = 2.000 J.

The final velocity is obtained from the equation
W = ½mVf2 - ½mVi2, where Vi = 0.

2.000 J = ( ½ )(1000 kg)Vf2, from where Vf = 2 m/s.

Physics Homework, Visit Sites:
· Energy, Work and Power: Concepts
· Kinetic Energy
· Potential Energy
· Power