Which branch of government determines the speed limit on interstate highways?

The federal government.

Explanation:

Interstate highways are the roadways that connects different states and gives access to travelers to go across different states. They are the main roadways to get to another state without the need to have any restrictions.

Speed limits are the limits at which a vehicle is allowed to run, differing across various types of vehicles and the roadways involved. The speed limits of the interstate highways are determined by the federal government who makes up the limits for the vehicles to be legally allowed to ply. Different states have different speed limits, all of which are determined by the federal government, which surprisingly, is rather unknown by most people.