When a body is moving in a straight line and its speed is increasing, then the magnitude of its velocity vector is getting larger and larger. Since acceleration is the change in velocity, the acceleration must be lengthening the velocity vector. Thus, it must be in the same direction as the velocity vector. In the animation below, the acceleration is shown with an imaginary arm, with which it is pulling on the velocity vector, making its magnitude longer.
Whenever an object is moving in a straight line and speeding up, its acceleration is in the same direction as its motion.