Wheel lockup

Start with identifying the brake system your car has.
Also try to identify which wheel or wheels lock up.
Lock up caused by rapid hard application of the brakes is normal in some circumstances. So keep track of the exact situation the wheel or wheels locked up under.
Do a visual check. Start with condition of the fluid in the master cylinder. Then check the brakes on each wheel.

Factory options on a '73
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from The 1970 Hamtramck Registry - 1973 Dodge Dealership Data Book - Dart
The 1970 Hamtramck Registry - 1973 Plymouth Dealership Data Book - Valiant/Duster

If you find larger diameter front drum brakes, that was a running change. See the service bulletin under brakes
The 1970 Hamtramck Registry "1973 Plymouth, Chrysler & Imperial TSBs" Page

Service manual for '73 Dodge (can use as substitute for Plymouth FSM)
MyMopar - Mopar Forums & Information - Service Manuals

Chrysler Master Tech videos and booklets.
Master Technician Service Conference - Chrysler's Training for Mechanics
same in a different format
MyMopar - Mopar Forums & Information - Browser MTSC by Topic - Brakes