2.1.6—Derive, from the definitions of velocity and acceleration, equations that

If acceleration a is constant, integrating a=dv/dt gives v=u+at; integrating v=ds/dt then gives s=ut+½at² and v²=u²+2as.

The derivation assumes constant a and consistent initial conditions. Use the equation containing the known quantities and keep displacement signed.

Eliminating t from v=u+at and s=½(u+v)t yields v²=u²+2as.

These equations cannot be used unchanged when acceleration varies with time or position.