1: Camera won't take a photo at a fast shutter speed
You don't have enough light - the faster shutter speeds let in only a tiny amount of light and your camera might just refuse to take a photo if there isn't enough light. Try at 1/500th and see if you can get the effect you want, otherwise go outside during the day in a well-lit place.
It can be hard to keep your focus on the subject when the subject is fast-moving. Don't worry too much about the focus for this exercise. As long as you can take 2 photographs, 1 with a blur and 1 without, it doesn't matter if your focus is off.
3: ISO is too high
Don't know what ISO is? Don't worry, we'll cover it next week. Otherwise, yes, your ISO will probably shoot up to compensate for the tiny shutter speed. Don't worry about it - this is an exercise in extremes.
4. Image is too dark or too light
You might just have reached the mechanical limits of your camera. If your image is too dark, try somewhere lighter, or try using a slower shutter speed. If your image is too light, try somewhere darker, or try using a faster shutter speed.
Part of the point of this exercise is to see what effect hand-holding your camera has on blur and camera shake at different shutter speeds. Don't delete all your blurred images - they are part of the learning journey.
A More advanced project
Create an image you are pleased with, where you have a long shutter speed and you deliberately move the camera.
A YEAR WITH MY CAMERA
If you've stumbled on this page by accident, you are reading part of Emma Davies' free beginner's photography workshop. For all the details, and to sign up, go to AYearWithMyCamera.com.