The correct option is (c).
Explanation
Velocity is a vector quantity, characterized by both magnitude (speed) and direction. For an object to maintain uniform velocity, both its speed and its direction of motion must remain constant throughout the motion.
Statement 1 is Correct:
Acceleration is defined as the time rate of change of velocity. If an object is moving with uniform velocity, its velocity does not change with time (neither in magnitude nor in direction). Therefore, the change in velocity is zero, which implies that the acceleration is zero.
Statement 2 is Incorrect:
By definition, uniform velocity implies that an object covers equal displacements in equal intervals of time, however small these time intervals may be. If an object covers unequal displacements in equal intervals of time, it is moving with variable (non-uniform) velocity.
Statement 3 is Correct:
Motion along a circular path involves a continuous change in direction at every point. Since velocity is a vector quantity dependent on direction, a change in direction constitutes a change in velocity, even if the speed (magnitude) remains constant. Thus, uniform velocity is not possible in a circular path; such motion is always considered accelerated motion.
Key Takeaway:
Uniform velocity strictly requires constant speed in a straight line. In curvilinear or circular motion, the direction changes continuously, making the velocity non-uniform and the motion accelerated.