A particle travels in a spiral path with constant speed, as shown...

For a particle moving with a constant speed $v$, the tangential acceleration is zero ($a_t = \dfrac{dv}{dt} = 0$).

The only acceleration acting on the particle is the normal (centripetal) acceleration, which is responsible for changing the direction of motion. The magnitude of this acceleration is given by:
$a = a_n = \dfrac{v^2}{R}$
where $R$ is the radius of curvature of the path.

From the given figure, as the particle moves along the spiral path in the direction indicated by the arrow, it moves from the inner, tighter loops to the outer, wider loops. This means the radius of curvature $R$ of the path is continuously increasing.

Since the speed $v$ is constant and the radius of curvature $R$ is continuously increasing, the magnitude of the acceleration $a = \dfrac{v^2}{R}$ must decrease continuously.