Answer:
First of all, what is acceleration? — Acceleration is the rate of change of velocity per unit of time.
Now, we know that velocity is a vector quantity i.e we need both magnitude and direction to define it and so is acceleration. We can now say that in acceleration, the direction of motion is very important or to define acceleration we need both the magnitude of motion (here it is the speed) and its direction.
Now coming to your question. There are two possible answers to this question.
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,Case 2 — When the body is not moving in a straight line or is constantly changing its direction. In this cas the speed still is constant but the direction is constantly changing, for example in the case of a circular motion the direction of motion constantly changes (the direction of a moving body in a circular path at any point is the direction of the tangent of the circle at that point). Hence the velocity changes as the body move along the circular or curved path.
Now, as I earlier mentioned to define acceleration we need to know it's magnitude and it's direction, and acceleration is the rate of change of velocity per unit of time — the speed remaining constant the direction constantly changing, and the velocity changes at different time intervals or rate of change of velocity is ≠ 0 unlike in case 1. Since there is the of and a change in velocity (speed constant but the direction is changing) there is some acceleration.
To sum everything up — in the case of linear motion i.e motion in a straight line when the speed is constant and direction is not changing, velocity will be zero and hence acceleration would be zero. In case of a non-linear motion i.e motion not in a straight line, in a circle or any path where the speed is constant but the direction is constantly changing, velocity will not be zero and hence the acceleration would not be equal to zero. Either it would be greater or less than zero.