If it's a DC motor, you can use an SCR (Silicon Controlled Rectifier).
If it's an AC motor, you can use a TRIAC.
You can also use mechanical relays, or solid state relays, or Mosfets.
Since it's line voltage, might also help to have some physical isolation between your low voltage electronics and the high voltage section (for added safety). You can use "optical" equipped mosfets, etc... basically, your low voltage electronics turns on a small LED (inside the mosfet), and the light emitted is detected, which then switches/turns on the high voltage side of the Mosfet (everything happening internally).