Runway Length for Takeoff: Solving for x

[stanners]

Homework Statement

A 727 jet needs to attain a speed of 200 mph to take off. If it can accelerate from 0 to 200 mph in 30 seconds, how long must the runway be? (Assume constant acceleration). Show all your work and include units in your answer.

Homework Equations

The Attempt at a Solution

Since v = dx/dt = 200t

I took the integral of dx = integral of 200t dt

and I got x = 100t^2 + C

So I plugged in 0.5 as t and got x = 25.

So x = 25 miles? But.. 25 miles sounds wrong for an airplane runway.. where did I go wrong?

 

[Dick]

You have time units of both hours, minutes and seconds in your problem. I would suggest before mixing them (and not indicating units) that you convert your numbers to a common time unit.

 

[stanners]

Oh, so instead of 0.5, it should've been

( (30sec) / (3600sec/hr) ) = t

so it comes out to 0.0069 miles?

Thanks again

 

[Dick]

0.0069 miles=about 35 feet. About as bad an estimate as 25 miles. Just convert everything to seconds. You are doing everything correctly mathematically - except the grasp of units is horrible.

 

[Dick]

If you've ever taken off in a plane you know the answer is roughly on the order of a mile. Don't rest until you get something in that ballpark.

 

[stanners]

Actually, I don't even think I set it up right after I look at it again, so I'm stuck now.

v is not 200t (is it?). v is just 200. so dx = 200 dt,
so, x = 200t

so (30/3600) hour = t

plugged it in, got x = 1.6666666666667

so about 2 miles, that seems right. So did I actually set the problem up wrong?

 

[Dick]

Still wrong. Please start using units, ok? v=at. d=(1/2)*a*t^2. You had it set up just fine. The units are killing you. What it 200 mph in miles/sec?