The answer, like most things in photography, is that it depends. If you're a pixel peeper, you may be surprised at just how high a shutter speed you'll need to use to get a moving subject tack sharp. However if you're resizing a 24Mp image for the web, or printing it at 300 DPI to 8x10, it will be far less critical.
The distance of your subject and the focal length of your lens are factors as well. The closer your subject is and the longer the focal length of your lens will exaggerate movement due to a smaller linear field of view. So how do you know where to start?
You can of course experiment until you're blue in the face, but if you dust off a little of your high school trigonometry skills, you can easily calculate your field of view, and how much your subject is moving across it given its speed, distance, and the focal length and shutter speed used.
I was going to write an app to do this but decided it was probably more transparent (and a lot less work) to simply throw together a spreadsheet to calculate the amount of pixels your subject will be dragged across your shot given the parameters discussed above.
This simple spreadsheet requires you to know and enter the width of your camera's sensor in millimeters, and the number of pixels in the width of the image captured. For a typical Nikon 24Mp DX crop sensor these are 23.5mm and 6000 respectively. If your camera is different you can look up these two specs in the manual or search the net.
Once you have those you need to approximate the distance of your subject and the speed it is traveling across the frame. These can be in feet and feet/sec, or meters and meters/sec, so long as they are both the same. Then enter the shutter speed and lens focal length and the spreadsheet will calculate the angular field of view in radians, The linear field of view in feet/meters, the relative movement on the sensor during capture, and the number of pixels that the moving subject will be blurred.
There is also a "Keep Below" number calculated from the sensor's diagonal/1500 CoC method. This number is a best guess at what will be noticeable on an 8"x10" print viewed from 10 inches. This method will be a bit conservative for crop sensor cameras.
This spreadsheet was created in Apple's Numbers app, and is available for download in Numbers or Excel format. If you want to use it on your mobile device you could upload the Excel version to Google Sheets or use some Office like app on your device to access it.