The easiset way for you to do this is to actually use the Movement camera/zoom effect on the clip set for the whole length of the clip - make this the first effect you add to a clip.
Once this is done, keeping the clip selected, you should see the Keyframe bar just below the Effects pane with 2 diamond shaped markers on it - this assumes you have no other effects applied to the clip
You can drag these markers to alter the time when the zoom starts - the left marker.
Dragging the right marker to set how quickly it takes to zoom - the closer to the left marker the faster the zoom.
You could actually use the movement template if you split your clip, apply the zoom effect and then speed up the segment with the zoom using the "speed" effect.
If you are not familiar with keyframes, here is a good tutorial to give you a better understanding. It is not specific to the Zoom effect but it does show you the basic steps and where the markers are located.
These pictures will help with the start and end markers of the zoom effect.
Here is an image with the zoom applied and the Keyframes for the zoom highlighted.
The left diamond is at the start of the clip and the right diamond the end of the clip - the zoom effect will take the entire length of the image ( 7 secs) to go from the initial size to the zoomed in section.
In this image I have dragged the left marker so it is now 2 seconds after the start of the clip and the right marker has been dragged to 5 sec after the start of the clip ( it was at 7 secs in the above)
If you play the clip it stays at its original size for 2 secs, zooms in for 3 secs and then hold the final size for 2 secs as you can see in this short video .
Any jerkiness is a result of the video conversion process!! Try it yourself and you will find the zoom is smooth.
No it is Trier in Germany, looking towards the market place and St Gangolph's church (best set of bells I have ever heard) from the top floor of the Porta Nigra