Can object have a varying speed if its velocity is constant? Can it have varying velocity if its speed is constant? If yes, give examples in each case.

Speed is a scalar quantity Velocity is a vector quantity Velocity therefore has two parts to it, the magnitude which is the speed, and the direction for that motion.

Here's your example: You are going on a highway at a constant velocity 100 mi/hr east, and since the velocity already includes speed as a magnitude, the speed is also constant but has no direction.

Second one example: You are going around a circular track at a constant speed of 10 mi/hr. Since, it's a circular track, will the direction of your travel be the same? Therefore, in this case the magnitude of velocity which is speed is constant, but the velocity changes due to the change in direction.

Yes, an object can have a varying speed even if its velocity is constant. This occurs when the object moves along a curved path, such as a circular track, while maintaining a constant velocity. Since velocity is a vector quantity comprising both magnitude and direction, if the direction of motion changes while the magnitude of velocity remains constant, the speed will vary. For example, consider a car traveling around a circular racetrack at a constant speed of 60 miles per hour. As the car moves along the curved path, its speedometer will indicate a constant speed, but its actual speed relative to the ground will vary due to changes in direction.

Similarly, an object can have varying velocity even if its speed is constant. This happens when the object moves in a straight line but changes its velocity by changing direction. Since velocity accounts for both speed and direction, if only the direction changes while the speed remains constant, the velocity will vary. An example of this is uniform circular motion, where an object moves in a circular path at a constant speed. Although the speed remains constant, the velocity changes continuously because the direction of motion is constantly changing. For instance, consider a satellite orbiting the Earth in a circular orbit. Even though its speed remains constant, its velocity is constantly changing because the direction of its motion is continuously changing as it orbits the Earth.