How long does it take for a horse to reach top speed? Like how fast can they accelerate up to top speed?

I know their top speed but I wanna know how fast can they get up to that

?2021-01-28T00:48:55Z

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Some thoroughbreds accelerate throughout the entire race, and so reach top speed at the end. Consider Secretariat's performance in the 1973 Kentucky Derby, in which he ran successive quarter miles in 25 1⁄5, 24, ​23 4⁄5, ​23 2⁄5, and 23 seconds.

But since that first split is so close to the other splits, it tells us that (championship) horses reach (something like) top speed very quickly -- on the order of a couple of seconds.