The hydrogen balloon fixed inside an accelerating vehicle will move in the direction of acceleration because the heavier air will tend to rest in place opposite the acceleration, due to inertia.
A balloon on a vehicle will be subject to wind effects and vortices.
First, helium is less dense than air and this means there is a buoyant force upwards (it will float up). In the same way, air is less dense than water and so a balloon full of air forced under water will float to the surface.
In this analogy the car is a full plastic water or soft drink bottle and
water in the bottle = air in car, and air in bottle = helium in car.
If you take a full plastic bottle of water or soft drink you will notice an air bubble in it. Now give it a quick jolt (acceleration) and watch the air bubble move. Immediately, you will see the bubble move to the front and the liquid to the back. You can also start running with the bottle then stop suddenly. The air bubble will move to the back first, while the liquid goes to the front.
This involves Newton's first law of inertia, where an object at rest or in motion want's to remain in its current state until an external force acts on it.
In the case of acceleration, the water and air want to stay where they are (towards the back as the bottle moves forward) so the more dense water ends up at the back and the less dense object, which has to go somewhere, gets displaced towards the front. In the case of deceleration, the water is in forward motion and wants to stay that way (inertia) so when you brake it keeps travelling forward, thereby forcing the less dense air bubble to be displaced to the back.
The car behaves like the bottle but now the water becomes the air in the car, and the air in the bottle is the helium balloon. When you accelerate, again both objects want to remain where they are. So as the car moves forward the denser air ends up towards the back and the helium is displaced forward. When you decelerate, the denser air continues to move forward and the helium balloon goes backwards.