Formula: Uniformly Accelerated Motion Distance Time Acceleration
$$\class{green}{\Delta x} ~=~ \frac{1}{2} \, \class{red}{a} \, ( t_2 ~-~ t_1 )^2$$
$$\class{green}{\Delta x} ~=~ \frac{1}{2} \, \class{red}{a} \, ( t_2 ~-~ t_1 )^2$$
$$\class{red}{a} ~=~ \frac{2 \, \class{green}{\Delta x} }{(t_2 ~-~t_1)^2}$$
Distance
$$ \class{green}{\Delta x} $$ Unit $$ \mathrm{m} $$
Distance \( \Delta x = x_2 - x_1 \) covered by a uniformly accelerated object within the time \( \Delta t \). The object has had an initial velocity \( v_0 = 0 \) at the start of the acceleration.
Time
$$ \class{brown}{\Delta t} $$ Unit $$ \mathrm{s} $$
After this period of time \( \Delta t = t_2 - t_1 \) the body has covered the distance \( \Delta x \).
Acceleration
$$ \class{red}{\boldsymbol a} $$ Unit $$ \frac{\mathrm m}{\mathrm{s}^2} $$
Constant acceleration with which the object is accelerated uniformly.
- Positive acceleration means that the object is increasing in speed.
- Negative acceleration means that the object decreases in speed (brakes).