Your car shaking when you accelerate can be caused by several common issues:

• Unbalanced or uneven tires: Tires that are not evenly balanced or have uneven wear can cause vibrations while accelerating. Tire balancing and proper wheel alignment can fix this.
• Worn-out spark plugs: Dirty or failing spark plugs cause engine misfires, leading to shaking during acceleration.
• Damaged CV joints: Inner CV joints on the axle transfer power to the wheels. If damaged, they cause vibrations that worsen with acceleration.
• Broken motor mounts: Motor mounts hold the engine in place and absorb vibrations. If they are broken, the engine's movement causes shaking.
• Bent axle or driveshaft: Accidents or impacts that bend these components can cause severe shaking.
• Loose lug nuts: If wheel nuts are loose, the wheel can wobble and shake as you speed up.
• Transmission issues: Problems like low transmission fluid or damaged parts can lead to shaking when accelerating.
• Stuck brake calipers: Can cause shaking, especially if shaking occurs at certain speeds.

It's important to get these problems checked by a mechanic because driving with such issues can be unsafe and cause further damage to the vehicle. Initial diagnostics typically include inspecting tires, spark plugs, engine mounts, axles, and the transmission system to find the exact cause.