It is acceleration in the horizontal direction. This would happen as a result of a net horizontal force acting on a body.
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Acceleration
Zero.
The graph you described is a speed-time plot. If the line is horizontal, that indicates no change in speed over time. In other words, there is no acceleration (acceleration is zero), since there is no change in speed.
Constant speed ... zero acceleration.
-- constant acceleration -- speed increasing at a steady rate -- distance increasing as the square of the time since everything started