How to use mongodb aggregation?

Use the following aggregation pipeline which does an initial $match to filter out those documents that are less than 60.

The next pipeline step uses the $sort operator to re-order the documents by the time field which is necessary for the next step, i.e. the $group pipeline. In here that's where you derive the start and end fields through the use of the $first and $last accumulator operators that extract the first and last times when you group the documents by the speed field as the key.

The last pipeline step $project creates the additional field, duration using the $subtract arithmetic operator which, as the name implies, subtracts the start from the end times. The final pipeline would look like this:

db.test.aggregate([
    { "$match": { "speed": { "$gte": 60 } } },
    { "$sort": { "time": 1 }  },
    {
        "$group": {
            "_id": "$speed",
            "start": { "$first": "$time" },
            "end": { "$last": "$time" }
        }
    },
    {
        "$project": {
            "_id": 0,
            "speed": "$_id",
            "duration": { "$subtract": [ "$end", "$start" ] },
            "start": 1,
            "end": 1
        }
    }
])

Sample Output:

/* 0 */
{
    "result" : [ 
        {
            "start" : 1446271010,
            "end" : 1446271010,
            "speed" : 67,
            "duration" : 0
        }, 
        {
            "start" : 1446271007,
            "end" : 1446271007,
            "speed" : 61,
            "duration" : 0
        }, 
        {
            "start" : 1446271008,
            "end" : 1446271008,
            "speed" : 62,
            "duration" : 0
        }, 
        {
            "start" : 1446271004,
            "end" : 1446271004,
            "speed" : 70,
            "duration" : 0
        }, 
        {
            "start" : 1446271003,
            "end" : 1446271003,
            "speed" : 68,
            "duration" : 0
        }, 
        {
            "start" : 1446271002,
            "end" : 1446271009,
            "speed" : 63,
            "duration" : 7
        }
    ],
    "ok" : 1
}

I am posting this because the existing answer add unnecessary $sort stage to the pipeline which will result in the drop of performance.

You need to filter out all document in your collection where speed is $gte 60 using the $match operator then $group your document by "speed" and use the $min and $max accumulator operators which respectively return the mimimum and maximum value for "time" for distinct group. From there you need to $projection stage in other to calculate to "duration" using the $subtract operator. Of course the .aggregate() method provides access to the aggregation pipeline.

db.collection.aggregate([ 
    { "$match": { 
        "speed": { "$gte": 60 } 
    }}, 
    { "$group": { 
        "_id": "$speed", 
        "duration": { "$sum": 1 }, 
        "start": { "$min": "$time" }, 
        "end": { "$max": "$time" }
    }},
    { "$project": { 
        "speed": "$_id", 
        "_id": 0, 
        "duration": { "$subtract": [ "$end", "$start" ] }, 
        "start": 1, 
        "end": 1 
    }} 
])

Which yield:

{ "start" : 1446271010, "end" : 1446271010, "speed" : 67, "duration" : 0 }
{ "start" : 1446271008, "end" : 1446271008, "speed" : 62, "duration" : 0 }
{ "start" : 1446271007, "end" : 1446271007, "speed" : 61, "duration" : 0 }
{ "start" : 1446271004, "end" : 1446271004, "speed" : 70, "duration" : 0 }
{ "start" : 1446271003, "end" : 1446271003, "speed" : 68, "duration" : 0 }
{ "start" : 1446271002, "end" : 1446271009, "speed" : 63, "duration" : 7 }