If the magnitude and direction of acceleration of a particle are both constant, the path of the particle will not necessarily be rectilinear (straight line). While constant acceleration does result in certain types of motion, such as rectilinear or linear motion under specific conditions, it is not the sole determinant of the path.
The path of a particle is determined by both its initial conditions (position and velocity) and the forces acting upon it. Constant acceleration alone does not guarantee a straight-line path because other factors, such as initial velocity and the presence of other forces, can influence the motion.
For example, if a particle initially has a non-zero velocity component perpendicular to the direction of constant acceleration, the resulting motion will be a curved path. This is because the perpendicular component of the velocity will cause the particle to deviate from a straight line.
Additionally, if there are other forces acting on the particle, such as friction or a gravitational force, they can affect the path of the particle, even if the acceleration due to these forces is constant.
Therefore, while constant acceleration is a necessary condition for rectilinear motion, it is not always sufficient to guarantee it. The overall path of a particle is determined by a combination of initial conditions, forces, and constraints acting upon it.