Let's say a sideways force deflects a particle traveling with speed v through a small angle Δθ. Then Δv=vΔθ, and the acceleration is
a=Δv/Δt=vΔθ/Δt
The distance travelled while the force is being applied is
vΔt=rΔθ
Solve the second displayed equation for Δt and plug it into the first equation. There ya go.