Physics homework QUESTION! PLEASE HELP!?

Question

Airplane A, starting from rest with constant acceleration, requires a runway 400 m 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.

a) How long must the runway be for airplane B?
Answer for this part was 1600 meters! What is part B?

b) If airplane A takes time 'T' to travel the length of its runway, how long (in terms of 'T') will airplane B take to travel the length of its runway?

Answer 1

2t

Answer 2

Kinematics equations for uniformly accelerated motion (when there is no initial velocity, as it is the case here):
v = a x t
x = 1/2 x a x t2
v2 = 2ax

In a) problem, we use the last equation, because there's no t involved in it. Both airplanes have the same acceleration, so we keep a, but write xA, xB and vA, vB instead. Because the take-off speed for B is twice as great as that for A, we write:
vB = 2vA
and
vA2 = 2axA
vB2 = (2vA)^2 = 2axB = 4vA2
We divide both equations, so a cancels, and we get:
4vA2/vA2 = 2axB / 2aA or xB = 4xA, so xB = 4x400 m = 1600 m.
(We can also think instead of writing equations - the distance is proportional to square of speed, so if the speed is twice as great, the distance is 4-times as great)

b) We use the first equations and use A and B:
vA = a x tA and vB = a x tB or 2vA = a x tB = 2 x a x tA, which means that tB = 2tA (twice as much time). We can use more iformal way of thinking here: double speed means double time (with the same acceleration).

Answer 3

For part a, 1600 meters is correct. Distance under acceleration goes as the square of velocity. For part b, twice as long. Same acceleration, twice the velocity, twice the time.