Why in the world do you want to know the modal and median instead of the average???
Modal is the data that repeats the most and obviously you have to take your times and speed often to do that. So if you stop 30 times you have 30 speeds between stops... pick the one that repeats the most, thats your modal speed.
The median is the value that is just in the middle... same problem, you have to stop and take your times and speeds in intervals, do the math and pick the data that is just in the middle. If you stop 20 times... calculate the speed between each of those stops, put them in order at the end of the trip and pick the data that is number 10... done.
The modal speed and the median speed might not be the same obviously either way I dont understand why you want to do this tho... well there you have it... good luck.