In circular motion the body has constant speed but not constant velocity? Why?
The physics definition of speed is just distance covered per unit time. The physics definition of velocity, however, is a combination of speed AND DIRECTION. In other words, physics treats speed and velocity as two similar, but distinctly different, concepts. A wind speed, for example, can be given as 10 miles per hour. Its velocity, however, would have to specify that it is 10 miles per hour from the North.
An object following a circular path can be covering the same distance along the circle's circumference with every passing minute, giving it a constant speed. To maintain a circular path, though, its direction must be constantly changing. Since a change in either speed OR direction means a change in velocity, the object's velocity is not constant.
Why is it useful to define velocity that way? Because Newton's laws of motion relate any change in VELOCITY (not just speed) to the application of a net force. Even though circular motion can be at a constant speed, its changing velocity requires that a (centripetal) force be present to deviate from a straight line and maintain its circular path.
Paul Walorski, B.A., Part-time Physics Instructor
'For the sake of persons of ... different types, scientific truth should be presented in different forms, and should be regarded as equally scientific, whether it appears in the robust form and the vivid coloring of a physical illustration, or in the tenuity and paleness of a symbolic expression.'