Can a bodys speed change without accelerating

Yes. Velocity is speed per unit of time with a direction vector telling you which way the object in question is moving. Acceleration is a change in velocity - in any part of velocity. If something like, say, a rock is in deep space (a zillion light years from anything) and it's moving along unaffected by any gravity or other forces, it has some velocity (some speed in a given direction, or is moving at some distance per unit of time in a given direction), but it isn't changing speed or direction. If something is moving without changing its speed or its direction (either of which requires a force to act on the object - to accelerate the object), it has zero acceleration. Such an object is said to have a constant velocity and will have zero acceleration. Certainly if an object is not moving, it has zero velocity and zero acceleration, but that's probably not what is being asked. It has velocity (zero) and no acceleration. To recap, an object can have a non-zero velocity and zero acceleration.