Im not sure if this answers your question as i dont think i understood it but...

if a body is in uniform acceleration then it moves in a straight line unless acted upon by an external, unbalanced force
No necessarily, in a projectile motion, the body is under a uniform downward acceleration and yet not moving in a straight line. This is because of the 2 components of velocity. From this example we can conclude that the motion of a particle is decided by the direction of velocity also. This can also be prover by the equations of motion, which show that a body under constant acceleration can change the velocity( magnitude /speed or both) , thereby changing the direction of motion of Te body. V = u+at Where acceleration is constant.
Also, in the case of uniform circular motion, the acceleration is constant and towards the centre of the circle. This is an example of a body moving in a circle under the action of uniform centripetal acceleration.