Fifty one runs had been put on the board by Warwicks who had won the toss before Ian Westwood was caught by Northeast for 18.
Then Ian Bell went for ten and Darren Maddy 39 as Warwicks dropped to 78-3 at lunch.
In the second session, Coles took out Rikki Clarke and Tim Ambrose before Cook captured the wickets of Chris Woakes and Jon Trott who top scored with 67.
Neil Carter, who hit one six in an innings of 43 was Cook's fourth wicket of the day as Warwicks were all out for 250.
In reply, Kent were 43-1 at stumps.