To derive the basic laws of motion, you need Calculus. The only types of problems possible without Calculus are constant acceleration problems. Most of the laws in physics are stated in Calculus notation. F=ma, was actully written by Newton as the force is the time derivative of momentum. This is why space ships can move. As you get deeper into Physics you find that most physical phenomina can be modeled by a differential equation, which you need Calculus to solve or appoximate. Even throwing a baseball or hitting a golf ball do not follow the simple approach shown in Physics textbooks without calculus. The Physics you can do with algebra alone is mysterious and almost useless. I do agree that as you get deeper into Physics you need much more complicated mathematics.
The basic math used in physics is algebra. However, many of the algebraic formulae used are the result of calculus, which becomes more import as you progress further in the science of physics, as does trigonometry. For still more complex physics, still more complex maths are required.