# Kinetic energy

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**Kinetic energy**

We saw on page 36 that, w here there are no opposing forces. a moving body needs no force to keep it moving with a steady velocity. If, however, a resultant force does act on a moving body in the direction of its motion, then it will accelerate and the work done by the force will become transferred to increased kinetic -energy in the body.

In order to calculate the kinetic energy of a body of mass m moving with velocity r, we begin by supposing that the body starts from rest and is acted upon by a force F (no friction or other forces acting).

This force will give the body a uniform acceleration a, and it will acquire a final velocity 1′, after travelling a distance x. These quantities. a. r. and x will be related by the equation 1’1 = u2 + 2ax (page 24). In accordance with the law of conservation or energy, the work done by the force F in pushing the body through distance x will become transferred to kinetic energy of motion in the body.

Thus, but therefore, substituting for F,

work done = ma

work done = force x displacement

=Fxx

F = ma

x x (1)

Applying the equation v2 = u2 + 2ax and remembering that u = a

v2 = a + 2ax

whence a

2x

Substituting this value of a in equation (1), we obtain,

v2

work done = m x – x x = kinetic energy

2x

or kinetic energy (k.e.) = tmv2 (in joules)

where

and

m = mass in kg

r = velocity in mls