A boy is sitting in a merry-go-round which is moving with a constant speed of\[10m/s\] . this means that the boy is
\[\left( A \right)\] at rest
\[\left( B \right)\] moving with no acceleration
\[\left( C \right)\] in accelerated motion
\[\left( D \right)\] moving with uniform velocity.

Hint: The boy is moving in a merry-go-round hence this is a circular motion. Speed is only about the magnitude, no direction involved here. But the velocity is a vector quantity having both magnitude and direction. So, if one of them changes velocity will change. Here in the problem, it has to be noticed if the velocity changes or not. Thereafter, considering the given options the correct option can be evaluated based on the situation of the velocity.

Complete step-by-step solution:
A boy is sitting in a merry-go-around that is moving at a constant speed of \[10m/s\]. The merry-go-round moves in a circular way. Therefore, the boy is moving in a circular motion. Speed is a scalar quantity having only magnitude.
Now let us consider the given options and find the right answer.
Option \[\left( A \right)\]: Since the boy is sitting in a merry-go-round and it is moving, therefore the boy is also in a motion called circular motion, not in rest. Hence this option is wrong.
Option \[\left( B \right)\]: When a particle is in a circular motion even it has a constant value of velocity but also changes its direction with every change in position. Here, since the boy is moving in a circular motion his velocity changes its direction. And, acceleration is the rate of change of velocity. Hence, the boy is moving with acceleration. So, this option is also wrong.
Option \[\left( C \right)\]: This option is right since the boy has the velocity that changes its direction not magnitude, therefore the boy is in accelerated motion.
Option \[\left( D \right)\]: a uniform velocity consists of constant magnitude as well as constant direction. Since here the direction of the velocity changes the boy is not moving with a uniform velocity. Hence this option is wrong.
Option \[\left( C \right)\] is correct.

Note: The change in velocity for the circular motion is called the centripetal acceleration having direction towards the center. Centripetal acceleration can be evaluated by $a = \dfrac{{{v^2}}}{r}$ , $v$ is the magnitude of the velocity and $r$is the radius of the circular path.
The force acting due to the centripetal acceleration is called the centripetal force. It has a direction also towards the center.