Question: Solving the 10000-meter run time problem with constant acceleration

[kylera]

Bloody textbooks and their odd answers...

I've tried to solve this problem, and I've solved through it, only to realize that my answer and the book answer are drastically different. A keen eye in the process would be most appreciated.

Question: A runner hopes to complete the 10000-meter run in less than 30.0 minutes. After 27.0 minutes, there are still 1100 meters to go. The runner must then accelerate at 0.20 m/s^2 for how many seconds in order to achieve the desired time?

My solution:
Initial velocity = the rate at which the previous 8900 meters was covered in 27.0 minutes = 8900/27.0 = 3.29e2 m/s
Final velocity = the rate at which the last 1100 meters must be covered in the last 3.0 minutes = 1100/3.0 = 3.7e2 m/s

I then used the 'final velocity' = 'initial velocity' + 'time' * 'acceleration' equation, and got what I thought was, and turned out to be, an absurd value for 'time' = 200(!) seconds. The book says '3.1 seconds'. Can anyone see my mistake here so far, or what I should've or should not have done? Much thanks.

 

[andrewchang]

your initial velocity is not in m/s- when you divided it, you got 329 m/minutes.

 

[kylera]

D'oh!

Thanks!