There are three particles shown in Figures I, II, and III. The velocity and acceleration vectors associated with the motion of three particles are shown. Which of the above could represent the velocity and acceleration vectors for a projectile following a parabolic path?

(A) I only
(B) II only
(C) III only
(D) I and II only

Hint: Projectile motion is a form of motion experienced by an object or particle that is projected near the Earth's surface and moves along a curved path under the action of gravity only. In projectile motion acceleration due to gravity is always acting downwards on the particle and the direction of velocity changes.

Complete step-by-step answer:
In projectile motion acceleration due to gravity is always acting downwards on the particle and the direction of velocity changes.
Hence, figures I and II can represent a projectile motion.
If we look at the figure I, here the velocity and the acceleration due to gravity are acting perpendicular to each other. Acceleration due to gravity which is acting in a downward direction.
Let’s discuss in figure II, in the figure, the velocity and acceleration due to gravity are acted on the body in such a way that the acceleration due to gravity is in a downward direction.

Now, if we look at figure III we see that velocity and accelerations are in the same direction. We know in this condition when velocity and acceleration are in the same direction the path of the particle will be a straight line. Therefore it cannot represent a projectile motion.
Therefore, the figure I and II depicts the projectile motion but III does not show the projectile motion.

$\therefore$ option (D) “I and II only” is the correct option.

Note:
Projectile motion is when an object moves in a bilaterally symmetrical, parabolic path.
Projectile motion only occurs when there is one force applied at the beginning, after which the only influence on the trajectory is that of gravity.
The projectile motion emphasizes one important aspect of constant acceleration that even constant acceleration, which is unidirectional, is capable of producing two-dimensional motions.
The basic reason for this is that the force and initial velocity of the object are not in the same direction.
Constant velocity means the object in motion is moving in a straight line at a constant speed.