Be careful not to use speed and velocity as though they are interchangeable. Velocity is a vector, and therefore has a magnitude and a direction. Speed is just the magnitude part of the velocity.
Acceleration is the change in velocity over a period of time. a = Δv/Δt If either the magnitude (speed), or the direction, of the velocity are changing, then there will be an acceleration.
For example, an object moving with uniform circular motion, would have a centripetal acceleration (directed toward the center of the circle) and constant speed, but its velocity would not be constant, because the direction of the object's motion is changing.
Another example would be an object tossed straight up. It would momentarily have zero speed (the magnitude of the velocity is zero) at the top of its motion, but the change in velocity is not zero, because the direction of the object's motion is changing from upward to downward.
