electric motor to carry a person

Hello, I'm planning on using an arduino to control and monitor an E-Bike. Will allowing the bike to shift through gears make the motor more efficient? For example, start the motor in a low gear, and shift up as rpm increases (basically a transmission). I know electric vehicles almost never have transmissions, but would this allow me to ride more diverse terrain? I.E. use a low gear for torque on hills, and a high gear for speed on flats. Thanks!

Yes, gears can help efficiency. For example, a stalled motor, or a motor with no load at all, has an efficiency of zero. http://www.farnell.com/datasheets/62656.pdf

Most e-bikes have gears for the pedal power but not for the motor. In most European countries you need a licence to ride an electric bike but not for an electrically assisted bike so pedals are a necessity.