Odd Vibration

I have a 5.0L 1990 Ford Bronco, 4x4, Eddie Bauer edition. It has a weird vibration only during acceleration and braking. When coasting the vibration does not occur. The vibrations speed is directly related to vehicle speed, and is not felt in the wheel or pedals. Any ideas?

Imo you have a driveline angularity problem.

Check the rear driveshaft U-joints for looseness, play etc. Also check the rear axle housing-to-spring bolts for tightness. Check the leaf spring mounts, bolts and rubber insulators.
Finally, check the leaf spring packs for bent or broken leaves.