How Long Did Boo Radley Accelerate to Finish the Race on Time?

[.benK]

Homework Statement

Boo Radley wants to run a 1500m race with an average velocity of 6.00m/s. After running the first 500 m, Boo notices that the elapsed time is 1 min 40 seconds. Panicking, he accelerates for "t" seconds at 0.20 m/s² and then finishes the race at his new faster speed. He makes it just in time. How long did he accelerate for? (Use 5 sig. figs. in your answer)

Hint: The answer is between 5 and 10 s.

The Attempt at a Solution

I figured out that he has 150 s to run 1000m, so I divided that and got 6.6666, then divided that by .2 and took the square root of that answer to get 5.7706s. Went to the teacher today and told me I was way off. I have tried to graph it as well, but I am just stuck and don't know what to do. PLEASE HELP.

 

[gabbagabbahey]

Hint: what does 1000m/150s actually represent?

 

[Hootenanny]

Homework Statement

Boo Radley wants to run a 1500m race with an average velocity of 6.00m/s. After running the first 500 m, Boo notices that the elapsed time is 1 min 40 seconds. Panicking, he accelerates for "t" seconds at 0.20 m/s² and then finishes the race at his new faster speed. He makes it just in time. How long did he accelerate for? (Use 5 sig. figs. in your answer)

Hint: The answer is between 5 and 10 s.

The Attempt at a Solution

I figured out that he has 150 s to run 1000m, so I divided that and got 6.6666, then divided that by .2 and took the square root of that answer to get 5.7706s. Went to the teacher today and told me I was way off. I have tried to graph it as well, but I am just stuck and don't know what to do. PLEASE HELP.

Welcome to PF,

You're spot on with there first bit, i.e. that he has to run 1km in 150s. However, after that I'm not sure what your doing.

How far as the runner traveled during the period in which he accelerates? What is his final speed? (I'm not looking for numerical answers, I'm looking for equations).

Moderation Note: I'm moving this to Intro. Physics.

 

[.benK]

Alright so, I got a breakthrough.. I think, here is what I have so far.

If he accelerates for 3 seconds he is already at 6.8 m/s time elapsed will be 103 seconds and he will have traveled 517.8 meters leaving 982.2 meters to complete. at a speed of 6.8 meters a second that will take him 144.44 seconds to complete the race giving an overall time of 247 seconds to travel 1500 m which is already 6.06 m/s...teacher said the answer is between 5-10

I know I'm on the right track but I'm not sure where to go next..

 

[.benK]

Oh yeah and didn't mean to put it into the advanced section. :P

 

[Hootenanny]

Alright so, I got a breakthrough.. I think, here is what I have so far.

If he accelerates for 3 seconds he is already at 6.8 m/s time elapsed will be 103 seconds and he will have traveled 517.8 meters leaving 982.2 meters to complete. at a speed of 6.8 meters a second that will take him 144.44 seconds to complete the race giving an overall time of 247 seconds to travel 1500 m which is already 6.06 m/s...teacher said the answer is between 5-10

I know I'm on the right track but I'm not sure where to go next..

As I said earlier you are indeed on the right track, however to progress further you need to start by answering the question I asked you:

How far as the runner traveled during the period in which he accelerates? What is his final speed? (I'm not looking for numerical answers, I'm looking for equations).

The question can of course be solved by 'trial and error', but this method is extreamly tedious and very inelegant. As I said above, I'm not looking for numerical solutions at this point (since exact solutions to my questions aren't possible), just equations.

 

[Kurdt]

He's not already traveling at 6m/s as you have assumed (plus 3 times 0.2 is not 0.8). Work out his average speed after the first 500m.