The condition in which a body moving with uniform speed has variable velocity is when the body is moving in a circular path.

Here's why:

* Speed is the rate at which an object covers distance. It's a scalar quantity, meaning it only has magnitude.

* Velocity is the rate at which an object changes its position. It's a vector quantity, meaning it has both magnitude (speed) and direction.

In circular motion, even if the object maintains a constant speed, its direction is constantly changing. This continuous change in direction means the velocity is changing, even though the speed remains the same.

Example:

Imagine a car driving around a roundabout at a constant speed of 50 km/h. Even though its speed is constant, its velocity is constantly changing because its direction is constantly changing.