linear acceleration in position keyframes

[John Br]

I am trying to animate an airplane accelerating down a runway. I need to have the background accelerate so it looks like the airplane is moving. I need a smooth linear acceleration. In the picture below I describe the acceleration I need with a red line.

 

Every kind of motion I can get seems to go faster than the second keyframe and then slow down. I need to start at zero and end at the second keyframe. Not go faster than the second keyframe then slow down. Every time I choose linear the motion goes from %0 to %100 in one frame.

I think it might have something to do with both the first and second keyframes but after over an hour of looking for answers online, I still cannot find an answer. 

Does anyone know what I can do to make this 0 to 100 acceleration?

[John Br]

I can make it do this:

 

[John Br]

Ok for the sanity of anyone else that finds this. After an hour and a half, I realized that it is a physics problem. You cannot start at a given point at a given time going 100 Kph and end at a given point in a given place and then say "I want to go more slowly for the first half of the trip and end up in the same place at the same time without going any faster than 100Kph." You have to accelerate to 125 Kph to make up for a lost time, hence that acceleration curve going faster than keyframe two. 

[John Br · Accepted solution]

For anyone else looking I found the answer, You have to make bezier curves for keyframes 1 and 2. Then slide keyframe one earlier in the timeline to allow for the extra time it takes that you are moving at a slower speed and the peak on the curve will drop down.