Solving for Takeoff Distance: Airplanes A & B

[penguins]

Homework Statement

Airplane A, starting from rest with constant acceleration, requires a runway 600m long to become airborne. Airplane B requires a takeoff speed twice as great as that of airplane A, but has the same acceleration, and both planes start from rest.

Homework Equations

a.) How long must the runway be, in meters, for airplane B?
b.) If airplane A takes time T to travel the length of it runway, how long (in terms of T) will airplane B take to travel the length of its runway?

The Attempt at a Solution

I tried multiplying the 600m runway by 2 to get the runway length for airplane B, but that answer is incorrect, I am not sure how to find the length of the runway with the information given in the problem.

 

[Simon Bridge]

Welcome to PF;
Sketch a velocity-time diagram for each aircraft.
Their accelerations are the same, but B needs twice the speed.
The area under the graph is the displacement.

 

[penguins]

How do you make a velocity vs time graph when you don't have the velocity or the time in the information given?

 

[SteamKing]

How do you make a velocity vs time graph when you don't have the velocity or the time in the information given?

You know that airplane A requires a speed of V in order to takeoff, therefore, airplane B must reach a speed of 2V before it can take off. You know that both aircraft have the same acceleration, and you know how far aircraft A must roll before reaching speed V.

If only there were formulas which related acceleration, velocity, and distance traveled! Where could a poor student find such information like this? In a textbook, perhaps? Maybe on the web?

 

[Simon Bridge]

You have to make up some marks on the graph.
Lets say that plane A's takeoff speed is v, put a mark roughly half-way up your velicity axis, and label it v.

Plane B's takeoff velocity is twice that, so put a mark about twice as far up the velocity axis and mark it 2v.

Lets say that plane A take time T to reach it's takeoff speed ... so put a mark about half-way along the t axis and mark it T.

You know the initial velocity of plane A - so you can draw a line from there to point (T,v).
Now you have a triangle - you are told that the area under that triangle is 600m.
You know the formula for the area of a triangle.

You know that the acceleration of plane B is the same as for plane A ... you should be able to take it from there.

Or you could just look up some equations and plug and chug.