Kinematic Equations

Constant-acceleration kinematics.

\[ v = v_0 + a t $$ $$ x = x_0 + v_0 t + \tfrac12 a t^2 $$ $$ v^2 = v_0^2 + 2 a (x - x_0) \]

Variable table

Symbol	Meaning
\(v\)	final velocity
\(v_0\)	initial velocity
\(a\)	acceleration
\(t\)	time
\(x\)	final position
\(x_0\)	initial position

Assumptions - Constant acceleration - Straight-line motion

Derivation Integrate \(a=\) constant once to obtain \(v\), twice to obtain \(x\).

Connections - Newton’s laws - kinematics