you could probably do this with particles, using an additive material and just spawning a ton of them over time with no motion. you would just move the emitter and it would drop them in a line.
If you want it to happen in an animation, select the object (or the faces of the object) you want the streaks to come from, create an emitter that emits from an object, then under particleShape > Render Attributes choose Particle Render Type > Streak, hit the "Current Render Type" button, and you can set the line width of the streak, the tail fade, and the tail size to adjust how the motion trail looks. Hope this helps.
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