Giving a minecart momentum with a piston

I am trying to setup a situation where I press a button and a minecart is pushed onto some powered track where it is then boosted up and giving a good speed.

This is what I tried (cross-section):

[P]M____

 ^ piston
   ^ minecart
    ^^^^ powered track

When I give power to the piston, the minecart gets shoved onto the powered track fine, however it just rests there. In order to get it boosted by the powered track, I have to manually touch it.

Is there a way to get the cart boosted automatically when it gets pushed onto the track?

This can be done without the piston at all.

If a cart is sitting on an inactive powered rail which begins receiving power, it will start moving as long as there is only one direction for it to go. This occurs if…

• …the powered rail is sloped (you will go downhill), or
• …the cart's travel in one direction is blocked by a wall.

You can use this to start from the end of a track by placing a wall:

Or in the middle of a track using a dip:

(Images courtesy of the wiki's page on powered rails.)