How to smooth my accelerometer-based character movement?

I am building an infinite vertical platformer for mobile platforms and I am using the accelerometer to move the player left and right. The further the device is tilted the faster the player moves across the screen. Currently my player is a little too shakey and I would like to create a more fluid movement across the screen. Here is my code to move the character:

 /********************************* Variables  **************************************/
 
     // Variables
     float jumpForce = 700f;
     float maxSpeed;
     float acceleration;
 
 /********************************* Start Method ************************************/

     void Start ()
         {
         acceleration = Mathf.Abs (Input.acceleration.y);
         }

 /********************************* Fixed Update  **************************************/
 
     void FixedUpdate () {
     
             if (acceleration < 0.2f) {
                 maxSpeed = 17;
             } else if (acceleration < 0.9f) {
                 maxSpeed = 25;
             } else {
                 maxSpeed = 40;
             }
         
         float move = Input.acceleration.x;
             rigidbody2D.velocity = new Vector2 (move * maxSpeed, rigidbody2D.velocity.y);
 
 /******************************* Collision Function ******************************/

     void OnCollisionEnter2D(Collision2D coll)
         {
             foreach(ContactPoint2D contact in coll.contacts)
             {    
                  rigidbody2D.AddForce (new Vector2(0, jumpForce));
             }
         }