"sprint for" is correct and can be used in written English.
It is mostly used to mean to run quickly to a certain destination. For example, "The kids sprinted for the playground."
Sprint for 30 seconds, drop to threshold level for 2 3 minutes, the sprint for another 2 3 minutes.
Take the men's team sprint, for instance.
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I just have to sprint for a full marathon.
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Next, you might sprint for 8 seconds, run while holding on to the bar for 10, then sprint for another 8.
Leaving the reservoir, DuBois would make a sprint for his office, followed by Stefansson and Andersen.
He was even disqualified from one intermediate sprint for what was deemed an illegal push.
Cadel Evans beat the defending champion, Ryder Hesjedal, in a bunch sprint for second place.
Instead of competing in a sprint for cash, candidates would vie for votes.
Now they have Bob Baffert watching their belongings while they sprint for their winner's circle.
