Position via constant acceleration and time

If a body is moving with a constant acceleration, its position in space is a quadratic function of time.

Conditions:

1. Acceleration is constant, i.e. \(\frac{d a}{d t} = 0.\)

Links:

1. Wikipedia, vector counterpart of this law.

final_position

position at time.

Symbol:

x

Latex:

\(x\)

Dimension:

length

initial_position

position at \(t = 0\).

Symbol:

x_0

Latex:

\(x_{0}\)

Dimension:

length

initial_speed

speed at \(t = 0\).

Symbol:

v_0

Latex:

\(v_{0}\)

Dimension:

velocity

acceleration

Constant acceleration.

Symbol:

a

Latex:

\(a\)

Dimension:

acceleration

time

time at which final_position is measured.

Symbol:

t

Latex:

\(t\)

Dimension:

time

law

x = x_0 + v_0 * t + a * t^2 / 2

Latex:

\[x = x_{0} + v_{0} t + \frac{a t^{2}}{2}\]