You didn't mention the age of the child. If the child is a toddler, then I would ask the pediatrician to give you some advise on how to help the child become comfortable. You may have to seek some professional help. The worst thing you can do is try to scare them into not being afraid. These phobias are very real to the child. And how you handle it can determine what type of life they will have. Trust is very important. You can't just say the dark won't hurt you because you don't know the reason they are afraid of it to start with. When I was a child I was afraid of the dark. As I became older, the fear became worse. I had a step mother who was so mean. I had a night light in my room and of course when the bulb would burn out, I was in a panic. She would usually send me to bed in the dark, yelling all the way. Today I realize my home was very safe, But when I was 8'ish, I was afraid of what I could not see. I imagined someone would walk through the wall, and it wasn't until I was an adult and married that I overcame my need to have a night light. By the way, I still don't like spiders. I hope you get the child all the help available. Please be sympathetic and supportive. Your child may overcome these fears, they may never overcome them. Good luck
Desensitize her to her fears. Vacuum: Have her sit on the couch and show her the vacuum but do not turn it on. Point out what every visible part of the vacuum is and explain what the vacuum does. Then, have her touch the different parts of the vacuum. After this, show her how to turn the vacuum on and have her turn it on. Convince her to push the vacuum. Go slowly and, eventually, she will lose her fear of the vacuum. Cars: Show her pictures of cars in her favorite color. Show her different kinds of cars, trucks, vans, buses etc. Tell her how important cars are and that they can take her places like the store, school, the park, etc. Have her sit in the car with you and have a picnic. Allow her to honk the horn, turn the wipers on and play with the radio. Then, plug her in and turn the car on. Tell her that cars are not toys, she should never get in one alone and she should never crawl under one or stand behind one. Later, turn the car on and have her stand outside the car with you so she can experience the noise while you explain car safety to her. Water: Play some fun games in the bathtub. Show her the shower and have her use it to make bubbles in the bath. Put colored bubbles in the water and use toys and such. You can even put on a swimsuit and get in with her so she isn't so afraid. Take her to places where she can play in a shallow pool and where you guys can look at waterfalls. Show her video's of water falls on youtube. Darkness: This is a common fear. Try playing games in the dark, leaving only a night light on. Try eating dinner by candle light and going outside at night to look at the stars. This will help her feel more comfortable with it being dark but she may still need a nightlight at night. Dust: Show her how to draw pictures in the dust. Explain to her that it wont hurt her. Then, show her how to get rid of the dust.