# Average Acceleration

Written by Jerry Ratzlaff 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

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

### Where:

 Units English SI $$\large{ \bar {a} }$$ = average acceleration $$\large{\frac{ft}{sec^2)}}$$ $$\large{\frac{m}{sec^2)}}$$ $$\large{ t_f }$$ = final time $$\large{ seconds}$$ $$\large{\frac{m}{sec}}$$ $$\large{ t_i }$$ = initial time $$\large{ seconds}$$ $$\large{ v_f }$$ = final velocity $$\large{\frac{ft}{sec}}$$ $$\large{\frac{m}{sec}}$$ $$\large{ v_i }$$ = initial velocity $$\large{\frac{ft}{sec}}$$ $$\large{\frac{m}{sec}}$$ $$\large{ \Delta t }$$ = time differential $$\large{ seconds}$$ $$\large{ \Delta v }$$ = velocity differential $$\large{\frac{ft}{sec}}$$ $$\large{\frac{m}{sec}}$$