Question

can a body have a constant speed and still have a varying velocity? explain with example

Answer 1

yes if the body is moving with uniform speed in a circular track
its speed remains constant but velocity is non uniform as the direction of body is changing every time

Answer 2

Hey There! 
The answer to your question is Yes.  
The simplest example is what we call Uniform Circular Motion  
Like, consider a car moving with a constant speed on a circular path.  

Here, the speed is constant, but the direction of car is changing continuously. As we know, velocity is a vector quantity, so as direction of motion changes, velocity also changes. 

Hope it helps
Purva 
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