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This is poor. It uses the argument "There must be a force" three times. A force is an interaction between two bodies, in this case the horse and the Earth. The upward force is unexplained and, as Alessio says, it is badly named. Should be 'contact' or 'normal' force. The forward driving force is explained as being because the horse is moving forwards - but this contradicts the First Law that you started with. Just because it is moving doesn't mean that there is a forward force. The force doesn't come from the horse's legs; it comes from the ground. Then friction is produced to explain why the horse isn't accelerating. This 'forces out of a hat' approach leaves most students confused.
This is a great video and very useful for revision and consolidation of balanced forces! I would have used the 'Normal' force on the horse example rather than the "Reaction" force you quote, but the animation and all other explanations are really useful. I added this resource to the @tesScience newsletter. Thanks for sharing.
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