[s]A typical answer to derive this is<br /><br />Consider a particle in uniform circular motion with constant speed, v, and radius, r.<br />In a short time interval dt , the particle moves from A to B.<br />Distance traveled in time dt &nbsp; &nbsp;= &nbsp;v.dt<br /><br />by definition of arc length <br />arc length &nbsp;A B &nbsp;&nbsp; &nbsp;  = &nbsp; &nbsp;r d<img class='tex' src="/demolab/smf/teximages/5/0/d/50d91f80cbb8feda1d10e167107ad1ff.png" alt="\theta" /><br /><br />therefore,&nbsp; v.dt&nbsp; &nbsp; &nbsp; =&nbsp; &nbsp; r d<img class='tex' src="/demolab/smf/teximages/5/0/d/50d91f80cbb8feda1d10e167107ad1ff.png" alt="\theta" /><br />&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;  (v.dt)/r&nbsp; =&nbsp; &nbsp;  d<img class='tex' src="/demolab/smf/teximages/5/0/d/50d91f80cbb8feda1d10e167107ad1ff.png" alt="\theta" /><br /><br />by definition of change,<br />&nbsp;  in vector form&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; dv = v[sub]f[/sub] - v[sub]i[/sub]<br />[/s]