A runner hopes to complete the 10,000-m run in less than 30.0 min. After running

Question

A runner hopes to complete the 10,000-m run in less than 30.0 min. After running at a constant speed for exactly 27.0 min, there are still 1,200 m to go. The runner must then accelerate at 0.2 m/s^2 for how many seconds in order to achieve the desired time? The answer is 6.3 s but I can't seem to get that! A runner hopes to complete the 10,000-m run in less than 30.0 min. After running at a constant speed for exactly 27.0 min, there are still 1,200 m to go. The runner must then accelerate at 0.2 m/s^2 for how many seconds in order to achieve the desired time? The answer is 6.3 s but I can't seem to get that!

Explanation / Answer

Given

Target distance DT = 10,000 m

Target duration t = 30 min

Solution

The runner has travelled from 27 min

The travelled distance D = DT – 1200

D = 10,000 – 1,200

D = 8800 m

Velocity with which he crossed this distance D is

u = 8800/27

u = 325.92 m/min

u = 325.92/60 m/s

u = 5.43 m/s

The time remaining t’ = t – 27

t’ = 30-27 = 3 min = 180 s

If he continue at this velocity for 180 s

He will be able to cross a distance 5.43 x 180 = 977.4 m

But he need to cross the distance 1200 m in 180 s

So his velocity should be

v > 1200/180

v > 6.67 m/s

If he accelerate at the rate 0.2 m/s2

6.67 < v

6.67 < u + aT

6.67 < 5.43+ 0.2T

6.67 – 5.43 < 0.2T

1.24/0.2 < T

6.2 < T

T > 6.2 s

So, the runner must accelerate for 6.3 s or more in order to finish the run under 30 min

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.