from typing import List


def _update_positions(r:  List[float],
                      v:  List[float],
                      a:  List[float],
                      dt: float
                      ) -> None:
    """Update positions using velocities and accelerations in place"""

    n_particles = len(r) // 3

    for i in range(n_particles):
        for k in range(3):           # x, y, z

            idx = 3*i + k
            r[idx] += v[idx] * dt + a[idx] * dt ** 2

    return None