Time-independent Velocity

The equations of Kinematics connect the dots between Position, Velocity and Acceleration.

Time is present in two equations and we can, using some mathematical trickery, put the two together in a way that we remove time.

We will do this after we make some initial conditions intended to make the math more simple.

$x = x_0 + v_0t + \dfrac {1}{2} a t^2$

$x = 0 + 0 \cdot t + \dfrac {1}{2} a t^2$

$x = \dfrac {1}{2} a t^2$

$\dfrac {2x}{a} = t^2$

$t^2 = \dfrac {2x}{a}$

$t = \sqrt{ \dfrac {2x}{a}}$

$v = v_0 + at$

$v = 0 + at$

$v = at$

$v = a \sqrt{ \dfrac {2x}{a}}$

$v = \sqrt{ \dfrac {2x a^2}{a}}$

$v = \sqrt{ 2x a}$

Published by Robert Sterling