Q: My car makes a sound like a loud fan when I accelerate after slowing down or stopping

It is possible that your engine is getting hotter than normal and is kicking the fan on harder to assist with cooling. It is likely that if the issue got any worse that a warning light may come on. I would recommend checking your coolant level to ensure it is full. I would also recommend having a coolant flush performed if you have not done what in the past 30,000 miles or so. Doing those couple of tasks should assist the engine with its cooling capabilities and may quiet that fan down. Another possibility is that the fan motor is starting to fail and causing noise while the fan is running. In this case, I would recommend to have it replaced once it quits working to avoid overheating the engine. Consider YourMechanic for your cooling system services as they can all be completed at your home or office.