How fast do you push a cart?! You address the child with words while coming to a stop. If they don't listen by that time, they need a little more correction.
Can you prevent the child from falling with words?
The point is that although you think it is perfectly fine and safe to let a child ride in the basket, I don't. I don't because children fall out of them all the time.
I still wouldn't call you negligent if your child got hurt while riding in the basket.