# Constant Acceleration

Written by Jerry Ratzlaff on . Posted in Classical Mechanics

Constant acceleration ( $$a_c$$ ) of an object is the constant rate in a straight line at which the velocity changes with respect to time.  These formulas can not be used if acceleration is not constant.

### Constant Acceleration Formula

$$\large{ v_f = v_i \;+\; \bar {a} t }$$

$$\large{ v_f ^2 = v_i ^2 \;+\; 2 \bar {a} d }$$

$$\large{ d = \frac { 1 } { 2 } \left( v_f \;+ \; v_i \right) t }$$

$$\large{ d = v_i t \;+\; \frac { 1 } { 2 } \bar {a} t^2 }$$

$$\large{ d = v_f t \;-\; \frac { 1 } { 2 } \bar {a} t^2 }$$

Where:

$$\large{ a_c }$$ = constant acceleration

$$\large{ \bar {a} }$$ = average acceleration

$$\large{ d }$$ = displacement

$$\large{ v_f }$$ = final velocity

$$\large{ v_i }$$ = initial velocity

$$\large{ t }$$ = time