Physically Incorrect

Here’s the solution to this puzzle.

The helium balloon will actually do the opposite and get thrown forwards as you press on the gas. At first, this is quite counter intuitive, since we’re all accustomed to being thrown backwards. There are several ways to reason about this, but let me give you an elegant solution: a Helium balloon tends to “want” to move opposite of gravity. After all, if you let go of such a balloon outside, it will float up - opposite of ‘down’, which is where gravity points - to the sky. This has to do with the fact that Helium is less dense than air, so it floats because of buoyancy. But the reason isn’t as important to the solution as the observation itself.

Now, when you accelerate, you’re creating “fake gravity”. If you accelerate forwards, you’re actually creating a fictitious force pointing in the other direction in the accelerating car’s frame. Given that, where will the Helium balloon naturally tend? That’s right, just opposite of the fictitious gravitational force, which is forwards. Put slightly different, it will ‘float forward’, just as it floats upwards in the Earth’s gravitational field.

Incidentally, The notion that acceleration and gravity are interchangeable is at the very heart of Einstein’s general theory of relativity. It’s called the (strong) equivalence principle, and states that inertial and gravitational mass are interchangeable. Einstein has called this observation the “Happiest Thought” of his life  - but that’s a different story, and a different puzzle.