# Kinetic energy

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