2D materials (2DMs) are fundamentally electro-mechanical systems. Their environment unavoidably strains them and modifies their quantum transport properties. For instance, a simple uniaxial strain can completely turn off the conductance of ballistic graphene or switch on/off the superconducting phase of magic-angle bilayer graphene. This article reports measurements of quantum transport in strained graphene transistors which agree quantitatively with models based on mechanically-induced gauge potentials. A scalar potential is mechanically induced in situ to modify graphene's work function by up to 25 meV. Mechanically generated vector potentials suppress the ballistic conductance of graphene by up to 30% and control its quantum interferences. The data are measured with a custom experimental platform able to precisely tune both the mechanics and electrostatics of suspended graphene transistors at low-temperature over a broad range of strain (up to 2.6%). This work opens many opportunities to harness quantitative strain effects in 2DM quantum transport and technologies.