Resting the camera on the dashboard of the car to keep it relatively stable would be a good approach. Then it's just the car's movement and the cars outside that will create the blur and not camera shake. This will have to be experimental as far as shutter speeds and exposure are concerned. Obviously night time would work best if I am going to record light streaks. The camera pointing at back seat and kids with blur outside?
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I have highlighted this image because I like how the image is simple yet effective at demonstrating how light can be used in photography. This image was created with a high exposure setting which would more light in the image such as the trail, The trail would've been created by a person walking along with a torch held above the ground.