Final answer:
The correct answer is (C) II and IV are correct. An object can have varying velocity without varying speed if it changes direction (like uniform circular motion). Also, an object can have non-zero acceleration without varying speed if it's accelerating towards a point but maintaining a constant speed along its path.
Step-by-step explanation:
The question poses four different scenarios regarding the relationships among speed, velocity, and acceleration. Let's analyze each:
- (I) Varying speed without having varying velocity: This is incorrect because velocity includes both speed and direction. If the speed varies, the magnitude of the velocity changes, hence the velocity varies.
- (II) Varying velocity without having varying speed: This is correct. An object moving in a circular motion at a constant speed has a continually changing velocity due to the change in direction.
- (III) Non-zero acceleration without having varying velocity: This is incorrect. Non-zero acceleration implies a change in velocity over time, whether in magnitude or direction.
- (IV) Non-zero acceleration without having varying speed: This is correct. An example is an object in uniform circular motion, which has a constant speed but is accelerating towards the center of the circle, changing its direction.
Based on this analysis, the correct answer is (C) II and IV are correct.