OR: Both the magnitude and direction of the acceleration of a body are constant. Will the path of the body be necessarily a straight line?
It depends upon the direction of the acceleration of the body. If the acceleration and velocity have same direction, then the path will be rectilinear. If their direction is opposite, then the path can again be rectilinear. However, if they make a certain angle with each other, then they form a curved path.
[Read: Motion in a Straight Line]
For example, in projectile motion, when a body is projected by making an angle with horizontal, the path of the projectile is parabolic [acceleration due to gravity acts vertically downward on the projectile].