Yes. In Aperture Priority, the camera meters the scene and chooses the shutter speed for proper exposure. On most DSLRs, that predicted shutter speed is shown before you shoot—typically in the viewfinder and/or on the rear/top LCD—after metering is activated, often by half-pressing the shutter button.

That behavior is the whole point of Aperture Priority: you set aperture (and often ISO), and the camera sets shutter speed. If you don’t see it, check your camera’s display options, since placement varies by model.

For your specific goal—freezing motion—a mode that prioritizes shutter speed may be better. Shutter Priority lets you choose the minimum speed you need, and the camera adjusts aperture. Another useful option, if your camera supports it, is Manual mode with Auto ISO (or TAv mode on some cameras), where you set both shutter speed and aperture and let ISO float to match exposure.