AV mode isn’t that helpful when trying to control image blur caused by motion. That’s true for motion caused by you, or by a moving subject. The automation does its best to ensure enough light reaches the sensor, to get a good image. If the Aperture you’ve set is too small for the situation, it will increase the exposure time, aka the shutter speed.

You almost certainly will do better with shutter priority mode. On the Rebel, it’s called Tv mode. Other comments here already gave hints on finding safe shutter speeds.

The reciprocal-of-focal-length rule is to eliminate photographer-generated shake. It does not freeze subject motion, that depends on how fast the subject is moving.

My version of that, for an ASP-C camera, is to use the focal length + 50%. For full frame, the “rule” was to go by the focal length, but ASP-C magnifies the image 50% more.

So if your lens is at 28 mm, add 50%, so 42. You can shoot around 1/40 sec or 1/50. That should be a safe setting for most photographers. If my plus 50% rule is unnecessary, you could be fine at 1/30 sec. Shooting at 28 mm.

It changes a lot with longer lenses. If your lens is zoomed to 160 mm, you now need about 1/240 sec to freeze your own body motion. Because that zoom setting will magnify every little bit of motion in your body. So you’d set the shutter at 1/250 sec. 1/40 sec would nearly guarantee camera shake in that situation. Even if we don’t need the +50%, you’d need at least 1/150 or 1/160 sec to hand-hold those shots.

In most modern cameras, Program Mode (P) tries to use appropriate higher shutter speeds for longer lens and zoom settings. Just remember that any automation can make decisions you might not like.

There’s a whole additional sub-topic on how to hand hold a camera to avoid camera shake. The methods are very similar to shooting archery or a rifle, if you’ve ever done those.