A linear motor is essentially a multi-phase alternating 
current (AC) electric motor that has had its 
stator "unrolled" so that instead of producing a torque 
(rotation) it produces a linear force along its length. The 
most common mode of operation is as a Lorenz-type actuator, 
in which the applied force is linearly proportional to the 
current and the magnetic field (F = i × B).

nirbhay's answer is absolutely correct. the jet 
trains in japan which can accelerate their speed 
upto 500km per hour 
are the best examples of linear motor. here the 
train acts as a linear rotor which is excited with 
3 phase supply and the rails act as a unrolled 
stator which contains short circuited cross bars.