Non-Linear Acceleration

Abstract

In this programme, we shall investigate problems of bodies which move under the direction of a force which is not constant. Also, we shall examine the problem of a body propelled by a constant force, but having a variable mass, such as a rocket. Remember the four equations of linear motion in Programme 1:

$$ x = \tfrac{1}{2}\left( {{v_0} + v} \right)t $$

((1))

$$ v = {v_0} + at $$

((2))

$$ x = {v_0}t + \tfrac{1}{2}a{t^2} $$

((3))

$$ {v^2} = v_0^2 + 2ax $$

((4))

and four similar and analogous equations for the motion of bodies in pure rotation. You were given a specific warning that they were to be used only when the acceleration of the body was constant. Now force, mass and acceleration are related by the fundamental Equation of Motion which is Newton’s Second Law:

$$ \Sigma \left( F \right) = m \times a $$

so it follows that acceleration will be constant only if the force and the mass remain constant.