Consider a particle in uniform circular motion with constant speed, v, and radius, r.

In a short time interval dt , the particle moves from A to B.

Distance traveled in time dt = v.dt

by definition of arc length

arc length A B = r d

therefore, v.dt = r d

(v.dt)/r = d

by definition of change,

in vector form dv = v[sub]f[/sub] - v[sub]i[/sub]

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