Here is an activity I used in my Math Calculus class to introduce tangents at a point.
I gave each student a copy of the video below.
Then, in groups of 2, students had to answer the following questions (which is part of the comments in the full YouTube video)
1) Watch the video
2) Determine the average speed for the first 5 minutes.
3) Determine the average speed for the entire trip.
4) At the end of the video, the speed of the vehicle is 109 km/h, explain any discrepancies from your calculation in part 3.
5) Determine the average speed of the vehicle after 15 min of driving.
6) Determine, with the least amount of error, the speed of the vehicle after 15 min of driving.
7) Explain, if any, the difference from part 5 and part 6.
Feel free to use, change as you seem necessary.
For the parts that is hard to see:
The time at each break in the bottom right corner is the total driving time to that point.
The distances at each break are -7.6 km/16.7 km/23.3km/32.1km
I do apologize the video is quite horrible with YouTube. The original is much better. If you require a copy of the original, email me and I can get you a copy.