i) Can a body have a constant speed and still have a varying velocity? (ii) Can a body have a constant velocity and still have a varying speed?

(1)

let us talk about it in simple terms
vector quantity- are the quantities which have magnitude & direction-velocity is a vector quantity because it has both
scaler quantity- are the quantities which have magnitude but do not have the direction- speed is scaler because it has the magnitude but do not have the direction
so if the speed is constant & object keeps on changing the direction then velocity will keep on changing , like if you rotate an object tied with rope at one end at constant speed,since the direction is cganging contineously so does the velocity

(2)

No, in order for the velocity to be constant, the speed has to be constant.
Speed is a scalar, meaning that it is just a number. (A car goes 50 miles per hour).
Velocity is a vector, which indicates that it needs a measure of its displacement and a direction.
(A car is going 50 mph to the east).

A body can have a constant speed but a changing velocity because the direction can change while the speed is constant. (A car goes 50 mph around a roundabout).
However, a body can not have a constant velocity with a changing speed.
A car can not be slowing down yet still be going the same speed and direction.

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regards

Ramesh

Dear Student,
Please find below the solution to your problem.

(1)Yes if the body is travelling with uniform speed in a circular track its speed remains the same but the velocity is non-uniform as the direction of the body is changing every time.
One simple example is what we call Uniform Circular Motion (Uniform circular motion can be described as the motion of an object in a circle at a constant speed). For example, consider a vehicle moving with a constant speed on a circular path. Here, the speed is constant, but the direction of the vehicle is changing continuously. As we know, velocity is a vector quantity, so as the direction of motion changes, velocity also changes.

(2) No, a body can not have its velocity constant, while its speed varies. Rather, it can have its speed constant and its velocity varying. For example in a uniform circular motion.
The velocity ofan object can be changed by:
Change of speed
Change of direction
And in a uniform circular motion, the direction isnot always the same, rather, it keeps changing. While the speed can remain the same. So in this way, the velocity can vary and the speed can be constant. But the vice versa is never possible.

Thanks and Regards