How to interpret acceleration in non-standard units like m/(half-s)/s

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kattahk
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The general unit if acceleration is meter per second per second.

Let's play with the unit of the standard acceleration due to gravity which is 9.8 meter per second per second.

Thus how acceleration can be explained if its unit is expressed as 4.9 meter per half second per second or 588 meter per second per minute or 35280 meter per second per hour.
 
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All you've done is change the units.

The dimension is still length/(time^2), so it's still an acceleration.
 
It's no more mysterious than the room I'm in being 8ft long, and also 2.4m long, and 0.0024km long. I can't communicate anything helpful by saying "it's this long", so we agree on a standard length and write a distance as multiples of that length. If we agree different standard lengths then the same distance is a different number of standard lengths.

Acceleration is a bit more complex because you've got a standard length and two standard time intervals to play with, but the principle is the same. The number doesn't mean anything on its own. The unit on its own doesn't mean anything. The number times the unit means the same thing whether you choose ms-2 or atto-parsecs per micro-fortnight per nano-year.