How to maximise stomach drop when driving through a dip I have a couple of young kids, and on our school commute each morning we drive through a dip in the road. The dip is probably about 5 meters deep (15 feet) and the speed limit in the area is 60 km/h (40 m/h). We find it great fun to pretend its a dip on a rollercoaster, and I've been trying to work out the most efficient pattern of accelerating / decelerating through the dip to maximise the "stomach-drop" effect. But I'd like to get science on my side!
How do I maximise the stomach-drop? When should I be accelerating, coasting or braking?

Above are some sample segments of the dip, if the recommended accelerating/coasting/braking phases do not match up please specify better segments
Right now my hunch is to accelerate to point B (as the dip starts), then coast / brake through to point C, then accelerate again to point E, then coast again. But if I can eke out even more stomach drop, I cannot wait to test it out on my kids!
 A: The "stomach drop" you are referring to is due to the centripetal force provided by the curved road. The maximum effect will be felt at the bottom most point of the dip. 
The force during the dip will be $mg$ plus a component of ${1\over 2}mv^2$. Hence to maximize force experienced, you can crank up mass and/or velocity of the vehicle.
My suggestion is that you accelerate from the start till the bottom most point (so as to have the maximum possible velocity) and then ease up towards the end. If possible you can take a bigger car or more people to increase the mass too!
A: After giving this way too much thought..
I believe a solution of the problem would be as follows. Consider a slightly updated "dip-chart":

Assuming constant acceleration going forwards, at points A, C & E the force acting on our stomach would just be gravity pulling it downwards at 9.8m/s:

As we start going into the dip (point A), the car starts getting an additional downward acceleration. Our stomach, being a bag of liquid suspended inside our body, is similar to a mass held in place by a pair of springs. As the car accelerates downwards, the stomach lifts "up". The maximum amount of "upward" lift is at point B:

As we continue on the curve toward point C, the downward acceleration of the car tapers off and we reach point C and our original balanced stomach:

Now as we climb up out of the dip, the acceleration of the car gains an upward direction too, and so the "slow to react" stomach is pulled downwards on its springs, reaching its maximum at point D:

Finally, we exit the dip at point E and once again have a resting stomach:

Now for maximizing the "stomach drop feeling" (via acceleration / coasting / braking)
If we acceleration between point A & point B, we add an additional sideways force onto our stomach spring. So not only does it "move upward", it will always move "backward" a little:

We then coast / maintain speed from point B to point C, and then from point C to point D we decelerate / brake to make our stomach get a horizontal forward movement:

That gives a final set of instructions as follows:


*

*Up to point A, maintain constant speed

*Point A -> B, accelerate

*Point B -> C, maintain constant speed

*Point C -> D, decelerate

*Point D -> onwards, accelerate back up to speed

