Constant Acceleration

Written by Jerry Ratzlaff on . Posted in Classical Mechanics

Constant Acceleration

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

\( v_f = v_i \;+\; a_c t   \)          \( final \; velocity \;=\; initial \; velocity \;+\;  \left(\; constant \; acceleration \;\;x\;\;  time \; \right)   \)

\(v_f ^2 =  v_i ^2  \;+\;  2a_c s   \)

\(s =  \frac { 1 } { 2 }   \left( v_f  \;+ \; v_i \right)  t \)          \( displacement  \;=\;   \frac { 1 } { 2 }   \left(  final; velocity  \;+ \;  initial \; velocity  \right)  time \)

\(s =  v_i t \;+\;  \frac { 1 } { 2 } a_c t^2  \)          \( displacement  \;=\;   initial \; velocity  \;\;x\;\;  time  \;+\;  \frac { 1 } { 2 }  \;\;x\;\;  constant \; acceleration \;\;x\;\;   time^2  \)

\(s =  v_f t \;-\;  \frac { 1 } { 2 } a_c t^2  \)          \( displacement  \;=\;   final \; velocity  \;\;x\;\;  time    \;-\;  \frac { 1 } { 2 }  \;\;x\;\;  constant \; acceleration \;\;x\;\;    time^2  \)

Where:

\(a_c\) = constant acceleration

\(s\) = displacement

\(t\) = time

\(v_f\) = final velocity

\(v_i\) = initial velocity

 

Tags: Equations for Acceleration