Arunner hopes to complete the 10,000-m run in less than 30.0 min. after running at constant speed for exactly 27.0 min, there are still 1200 m to go. the runner must then accelerate at 0.20 m/s2 for how many seconds in order to achieve the desired time

the runner run at constant speed for 27 min

and total 1200 m distance remains after that

distance moved = 10000 - 1200 = 8800 m

now the speed of the runner is

now he has to cover rest of the distance in 3 min

so he will accelerate for t s

so his final speed is

now time to cover the distance is 3 min

after solving above equation

t = 6.3 s

so it will accelerate for t = 6.3 s

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answer: 31, 5556. 952 seconds