A runner hopes to complete a 10,000 m race in a time of 30

Question

minutes. After running at a constant speed for exactly 27 minutes,
there are still 1100 m to go. The runner then accelerates at
0.2 m/s2 for how many seconds in order to achieve the desired
time?

Answer 1

The runner wants to go the remaining 1100 m in 3 minutes. That will require an average speed of 6.11 m/s. His speed for the first 2700 minutes was
8900m/(27*60 s) = 5.49 m/s.

If he accelerates for time T (seconds) and then maintains constant speed for 180-T seconds,
Final speed Vf = 5.49 + 0.2 T
Distance travelled in final 3 minutes
1100 = Vf*(180-T) + (Vf + 5.49)T/2

Substitute 5.49 +0.2T for Vf in the final equation and solve for T.

Answer 2

12.4