Posted by **Zack** on Sunday, August 30, 2009 at 9:50pm.

A runner hopes to complete the 10,000m run in less than 30 minutes. After exactly 27 minutes, there are still 1100m to go. The runner must then accelerate at 0.20 m/s^2 for how many seconds in order to achieve the desired time?

I get 80.9 but I know that the answer is 3.1 seconds. How do you get 3.1 seconds? (What formula/processes?) Thanks.

- Physics Problem -
**MathMate**, Monday, August 31, 2009 at 1:04am
Assuming he ran at uniform speed for the first 27 minutes. Then initial speed,

u = (10000-1100)m/(27*60)sec. = 5.494 m/s

Remaining time is 3 minutes, or 180 s.

Distance to run, S = 1100m

a = acceleration = 0.2 m/s

let t=time of acceleration, then

new speed=u+at

time to run at new speed=(180-t) sec.

Distance run during acceleration

=ut+(1/2)at²

Summing up distance run in 3 minutes,

1100 = ut+(1/2)at² + (u+at)*(180-t)

which simplifies to

t² -360t +10000/9 = 0

From which t can be solved using the quadratic formula as

t=3.113 sec. or t=356.887 sec.

We reject the second solution because it exceeds the 180 sec. limit.

- Physics Problem -
**Jeff**, Sunday, September 12, 2010 at 5:10pm
shut up!

## Answer this Question

## Related Questions

- physics - A runner hopes to complete the 10,000m run in less than 30 minutes. ...
- physics - A runner hopes to complete a 10,000 m race in a time of 30 minutes. ...
- Physics (Algebra Bit) - I still need help on my other question as well... A ...
- statistics - Let x denote the time taken to run a road race. Suppose x is ...
- Maths - Three runners run a 10 metre race. Each runner runs according to the ...
- math - A student athlete runs 3 1_ 3 miles in 30 minutes. A professional runner ...
- Physics - Runner A is running at a constant rate of 2.3 m/s when he passes ...
- Physics - An athlete wants to complete the 4000 m run in 12.0 minutes. After ...
- physics - Runner A is running at a constant rate of 2.3 m/s when he passes ...
- Physics-Check - In a marathon race, one runner is moving at 5.0 m/s passes a ...

More Related Questions