A Unity C# script to attach to a GameObject with a Rigidbody2D so that it can be paused and resumed.

PausableRigidBody2D.cs

using UnityEngine;

public class PausableRigidBody2D : MonoBehaviour {

  private Rigidbody2D body;
  private Vector3 savedVelocity;
  private float savedAngularVelocity;

  void Awake() {
    body = GetComponent<Rigidbody2D>();
  }

  public void Pause() {
    savedVelocity = body.velocity;
    savedAngularVelocity = body.angularVelocity;
    body.isKinematic = true;
  }

  public void Resume() {
    body.isKinematic = false;
    body.velocity = savedVelocity;
    body.angularVelocity = savedAngularVelocity;
    body.WakeUp();
  }

  public void Reactivate() {
    body.isKinematic = false;
    body.WakeUp();
  }
}