Answer:
(1) only
Explanation:
Let's analyze each option.
(1) [tex]\frac{d}{dt}|v|[/tex]
this quantity corresponds to the rate of change of the module of the velocity, so it is basically the magnitude of the acceleration. In a uniform circular motion, the magnitude of the (centripetal) acceleration is
[tex]a=\frac{v^2}{r}[/tex]
where v is the speed and r the radius: since both v and r can be constant, then this means that this quantity can be constant as well.
(2) [tex]v[/tex] (vector)
This quantity is the velocity. Velocity is a vector: this means it has both a magnitude (the speed) and a direction. In a uniform circular motion, the speed can be constant; however, we know that the direction is for sure not constant, since the object is constantly changing path: therefore, this quantity cannot be constant.
(3) [tex]a[/tex] (vector)
This quantity is the acceleration. Acceleration is a vector: this means it has both a magnitude (given by [tex]v^2/r[/tex]) and a direction. In a uniform circular motion, the direction of the (centripetal) acceleration is towards the centre of the circle, perpendicular to the velocity: however, since the object is constantly changing direction, this means that also the direction of the acceleration is constantly changing, therefore this quantity cannot be constant.
