[jeffreyH (OP)]

If we decided we wanted to get our spaceship up to one tenth of the speed of light and then let inertia take over how could we tell when the required speed was reached?

[Bored chemist]

Integrate the acceleration from whatever you think of as "stationary".
But the whole point of relativity is that the question's meaningless.
A tenth of the speed of light WRT what?

[jeffreyH (OP)]

Integrate the acceleration from whatever you think of as "stationary".
But the whole point of relativity is that the question's meaningless.
A tenth of the speed of light WRT what?

Yes. Exactly! WRT what?

[alancalverd]

Microwave or laser doppler shift will measure your speed relative to the source. If you are hurtling away from the solar system, measure the frequency of the 21 cm hydrogen line (or indeed any other spectral line) from the sun.

[jeffreyH (OP)]

Now that's an answer and a half.

[jeffreyH (OP)]

DIY hydrogen line mapping of the Milky Way and other structures is a very interesting topic. It has been done.
http://www.spaceacademy.net.au/spacelab/projects/hlineobs/hlineobs.htm
 

[yor_on]

You might presume that the universe has a common uniform motion, without defining that as a 'speed'. That won't tell you your own 'speed' though as the universe is expanding at the same time. The best thing might be to use your own sun as some standard of being 'still', and measure your new relative motion relative that.

I've been wondering about that one too Jeffrey, and the point seems to be that it's accelerating that change your motion, and there 'c' can't be reached. It's like you have two states, one is uniform motion the other is acceleration.  There is no real definition of what 'speed' is in a uniform motion, and neither would I say, in a acceleration.

There is a trick some use though. Picking a very distant star that 'doesn't move' as some reference of being 'still' and define it from there.