Why can't a space ship accelerate infinitely?

Because a space ship needs to carry fuel, and because that fuel needs to be contained in a fuel tank.

That need to carry the fuel needed to make the spacecraft accelerate leads to the very nasty ideal rocket equation,

$$\Delta v = v_e \ln \left( \frac {m_{\text{initial}}} {m_{\text{final}}} \right)$$

The initial mass is the final mass plus the mass of the fuel and oxidizer that will eventually be expelled. The final mass includes the mass of the fuel tanks, the spacecraft structure, and whatever tiny payload that can be carried on top of that. Another way to look at that logarithmic growth in change in velocity is an exponential growth in fuel mass.

More fuel means larger fuel tanks and more structure to hold everything together. A delta V of 2.3 to 3 times the exhaust velocity is doable. That corresponds to a vehicle whose mass is initially 90% to 95% fuel. Beyond that, there's not much hope for a single stage rocket.

What about a multistage rocket? While multistage rockets appear to escape the tyranny of the rocket equation to some extent, they don't. They just change where the tradeoff occurs, and they add their own brand of exponential growth problems. The Saturn V + Apollo spacecraft that brought humans to the surface of the Moon and back was essentially a six stage rocket. The vehicle that took off from the surface of the Earth was arguably that largest, most powerful machine ever built. The vehicle that splashed down in the ocean when the mission was over was a tiny little thing that could barely hold three humans.

The only way to escape the tyranny of the rocket equation is the age-old answer to the age-old question "*Doctor, it hurts when I do this: «bonk»*" The answer: "*Don't do that then.*"

Unfortunately, we don't know how to avoid the nastiness of the rocket equation. The only viable option currently that doesn't require carrying fuel is a solar sail. However, you can't accelerate forever with a solar sail because sunlight drops as the inverse square from distance to the Sun. Beyond solar sails? Now you're in the realm of science fiction.

The above assumes Newtonian mechanics. The relativistic rocket equation is far, far worse than the ideal (Newtonian) rocket equation. If the ideal rocket equation is evil, the relativistic rocket equation is evil incarnate. The relativistic rocket equation is one of the answers to the Fermi paradox.

In the case of concave down part

The fluid that was initially flowing would have to shift a little bit upwards where there already exists fluid that was any way moving in that direction so at close approach to the surface there is same amount of fluid moving through lesser space and then we know

A1V1 = A2V2

Hence velocity increases similar way you can think for lower surface

Hope you can visualise

## Best Answer

It's most likely that the radar gun is just locking on to a different vehicle. Depending on how it's filtering and processing the received signal, it could even be measuring the speed of a car going in the opposite direction.