When shooting moving objects you need to use either shutter priority mode or manual mode. To photograph moving people you shouldn’t need anything more than 1/100th second to freeze the movement although slightly higher may be required for fast running/sprinting subjects.
When it come to taking photos of faster moving subjects like, bikes, cars, motorbikes you may need shutter speeds of up to 1/1000th of a sec one or if they are going at extreme high speeds you may need something between 1/1500 and 1/2000th second.
When shooting moving objects, a technique used by many photographers called panning is used. This is taking a series of shots while turning you get a crisp subject but a blurred background. In order to ‘pan’ set your cameras auto focus to continuous AF and select a shooting mode of continuous in order to take a lot of photos on one push of the shutter button. Then point your feet in the direction the subjects going and as it comes towards you hold the shutter down and follow its movement by panning, keep the camera in a smooth curve. At least one photo should be in focus and have a creative blurred background. With practise, you’ll get good results.