You accelerate slowly enough

You can't decelerate fast enough or turn fast enough to avoid obstacles. The best radar on a moving object ever made is probably the AGP-81 radar on the F-35. It can only see 550 km ahead. Even if you built a miracle radar that could see 100,000 km ahead, at .1c you could not slow down or evade it in time.

You'd only have 3.33 seconds. If you go at lower speeds, if you go "only" at 1% of the speed of light, you'd still only have just 33 seconds. And at that speed, it would probably take you 6000 years to reach a planet that's 40 light-years away. And even then you have complications. Planets and even solar systems are not stationary objects. They are constantly orbiting and thus mobile. You essentially have to achieve pinpoint accuracy in your calculations from 40 light-years away where information is 40 years out of date.

Based on that data, you'd have to set up an interception point. Maneuvering could set you off course and then you'd have to waste even more fuel and time trying to catch up.

At a "slow'' speed of 1% of c, you'd probably require 6000 years to reach the planet. That's not feasible in the slightest economically and it's debatable if the crew of a ship could keep their shit together that long. Or even if a ship could possibly maintain supplies that long.

Your comment is like some person at the turn of the 20th century talking about how impossible it is with the current technology for man to ever cross the ocean in a jet

This mentality assumes that technology can be advanced infinitely. There are natural limits that might not be surpassed. There's no law in the sky that says that because you did air travel, you can also do space travel or break the law of momentum or inertia.

For example, Einstein(or Poincare perhaps) invented the theory of relativity in 1905. Quantum mechanics came into being by the 30s and 40s. There are four fundamental forces of nature: Gravitation, Electromagnetism, Nuclear strong force, and Nuclear weak force.

The latter three can be explained by quantum mechanics, the first can be explained by relativity. One of the greatest goals of physics is to develop a unified field theory that can explain all four and reconcile relativity with quantum mechanics. Einstein tried for the last 30 years of his life and failed.

Richard Feinman, John von Neuman, Edward Teller, Stephen Hawking, and countless other physicists and mathematicians of near superhuman intelligence have tried for over 70 years and failed. 160+ IQ geniuses from all over the globe have tried and failed to break this nut. Same with questions like why does time run forward or what form does matter take inside a black hole.

There are laws in the universe that simply can't be broken. Such is the sentence of God.

You can't break the speed of light while having rest mass. You can't travel back in time(in a sense you can travel forward) and you can't know if there's life after death.

The 19th and 20th centuries saw rapid technological advances because the low-hanging fruit had not been picked. It was not that difficult to discover the laws of magnetism or relativity. It's vastly harder in comparison to finding the secret of eternal youth or creating life from inanimate objects.

Science is not like the tech tree on a video game where if you invest money, train scholars and give them raw materials, it will continuously keep advancing.