My dude, velocity is a vector, if you accelerate a body in a perpendicular direction to its velocity, its velocity will change direction, but not magnitude.

Grab a yoyo, start spinning it around. You are constantly accelerating it towards your hand. If you stopped and let it loose, it would move in a straight line and break the window and mom would be sad.

No acceleration means constant speed in a straight line. If it does not go with constant speed in a straight line, it's being accelerated.