How to find a start and stop od a break in GPS tracker data?

I have a data from GPS tracker. Let's say something like:

CREATE TABLE IF NOT EXISTS `gps_data` (
  `id` int(6) unsigned NOT NULL,
  `speed` int(3) unsigned NOT NULL,
  `time` varchar(200) NOT NULL,
  PRIMARY KEY (`id`)
) DEFAULT CHARSET=utf8;

and some sample data:

INSERT INTO `gps_data` (`id`, `speed`, `time`) VALUES
  ('1', '5', '07:00'),
  ('2', '10', '07:10'),
  ('3', '0', '07:20'),
  ('4', '0', '07:30'),
  ('5', '0', '07:40'),
  ('6', '0', '07:50'),
  ('7', '20', '08:00'),
  ('8', '40', '08:10'),
  ('9', '15', '08:15'),
  ('10', '0', '08:32'),
  ('11', '0', '08:40'),
  ('12', '0', '08:52'),
  ('13', '12', '09:10'),
  ('14', '0', '09:25');

The question is how to find a time of first and last position with speed = 0.

So in my example I would like to have something like:

[break_start, break_stop]
[07:20, 07:50]
[08:32, 08:52]
[09:25, NULL]

Here is the Fiddle to better understanding: http://sqlfiddle.com/#!9/d79228/4

What I have started to try is:

SELECT `time` AS break_start, `time` AS break_stop  FROM `gps_data` WHERE `speed`=0;

One method in MySQL is to assign a group to each row. This group can be the number of non-zero values before the row -- all rows with adjacent zero values are in the same group.

In MySQL 8+, you can use window functions for this:

select min(time), max(time)
from (select t.*,
             sum(speed <> 0) over (order by time) as grp
      from t
     ) t
where speed = 0
group by grp;

In earlier versions, one method is a correlated subquery:

select min(time), max(time)
from (select t.*,
             (select count(*)
              from t t2
              where t2.speed <> 0 and t2.time <= t.time
             ) as grp
      from t
     ) t
where speed = 0
group by grp;

Here is a SQL Fiddle.