# Average Acceleration

on . Posted in Classical Mechanics

Average acceleration, abbreviated as $$\bar {a}$$, is the change of velocity over an elapsed amount of time.  Whereas, instantaneous accleration is the change of velocity at a specific point in time.  As an example, if a vehicle is initially traveling at 100 feet per second and slows down to 50 feet per second over 60 seconds, the average acceleration over 60 seconds is - 8.3 ft per second.  The equation and calulation for average acceleration is shown below.

## Average acceleration formulas

$$\large{ \bar {a} = \frac{ \Delta v }{ \Delta t } }$$

$$\large{ \bar {a} = \frac{ v_f \;-\; v_i }{ t_f \;-\; t_i } }$$

Symbol English Metric
$$\large{ \bar {a} }$$ = average acceleration $$\large{\frac{ft}{sec^2}}$$ $$\large{\frac{m}{s^2}}$$
$$\large{ \Delta t }$$ = time change $$\large{sec}$$ $$\large{s}$$
$$\large{ t_f }$$ = final time $$\large{sec}$$ $$\large{s}$$
$$\large{ t_i }$$ = initial time  $$\large{sec}$$  $$\large{s}$$
$$\large{ \Delta v }$$ = velocity change $$\large{\frac{ft}{sec}}$$ $$\large{\frac{m}{s}}$$
$$\large{ v_f }$$ = final velocity $$\large{\frac{ft}{sec}}$$ $$\large{\frac{m}{s}}$$
$$\large{ v_i }$$ = initial velocity $$\large{\frac{ft}{sec}}$$ $$\large{\frac{m}{s}}$$ 