Question

A runner 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

Answer 1

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

$v = \frac{d}{t}$

$v = \frac{8800}{27*60} = 5.43 m/s$

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

so he will accelerate for t s

so his final speed is

$v_f = 5.43 + 0.20 * t$

now time to cover the distance is 3 min

$1200 = (5.43*t + 0.5 * 0.2*t^2) + (5.43 + 0.20t)(3*60 - t)$

after solving above equation

t = 6.3 s

so it will accelerate for t = 6.3 s