Velocity, distance, time problem

[hbomb]

A runner of mass 58.1 kg starts from rest and accelerates with a constant acceleration of 0.87 m/s2 until he reaches a velocity of 5.90 m/s. He then continues running with this constant velocity.

How long does the runner take to run 193 m?


I already know mass has no relation to what I'm suppose to find here. What I first did was use v=v(initial) + at to find the time it takes to get up to 5.90 m/s. Then I found the distance covered during this time. I then used x=x(initial) + vt and solved for t to find the rest of the time from when the runner started to run 5.90 m/s up to the end of his 193 m run. Then I add the both times together. I get 32.71 s, but the answer is not correct. This is one of those online questions. What am I doing wrong?

 

[radou]

Okay, you can easily get the time t1 for the first (the accelerating) part as t1 = v / a. Further on, to get the length of the first part, use the equation s1 = 0.5a*t1^2. Then, you have 173 - s1 = s2, which is the length of the part the runner runs with constant velocity. So, you can easily get t2 = s2 / v. So, the total time equals t = t1 + t2. The answer I got was around 36, I hope that is correct.

 

[berkeman]

Homework questions need to be posted in the Homework Forums, not in the General Forums.

Having said that, I get more like around 36 seconds. Is that closer to the correct answer? Post all of your work, including the intermediate results, and we can look for errors. It sounds like you are using the correct approach.