# Aircraft runway question - Acceleration, Time and Final Velocity

1. Sep 16, 2013

### Molly1235

Question:

An aircraft of total mass 1.5 x 10^5kg accelerates at maximum thrust, from rest along a runway for 25s reaching the required take off speed of 65 ms^-1.

Assume that the acceleration of the aircraft is constant. Calculate the distance travelled in this time.

My attempt:

I know s = ((u+v)/2) x t
So I did 65/2 x 25 = 812.5m but u feel like this is too simple and acceleration should be involved here because it's given me the mass of the aircraft?

Many thanks!
Molly

2. Sep 16, 2013

### Staff: Mentor

Your result is right. If there is no additional question, you don't need the mass of the aircraft.

3. Sep 16, 2013

### CWatters

I get same answer as you.

It's constant acceleration so the SUVAT equations of motions can be used...

http://en.wikipedia.org/wiki/Equations_of_motion#SUVAT_equations

One of those is the equation you used.

Perhaps the mass was given for another part of the question? Do they ask you to calculate the thrust?

4. Sep 16, 2013

### Molly1235

Well there's another that asks of the length of the runway decreases, what should be changed to enable the aircraft to meet the same take off speed? The only thing I can think of is acceleration...

5. Sep 16, 2013

### Molly1235

Ah excellent! Thank you - I just quoted someone else with the sub question...think this may have something to do with the mass...

6. Sep 16, 2013

### PhanthomJay

Yes, and how would you change the acceleration??

Yes, but what?

7. Sep 16, 2013

### Molly1235

Would you have to increase the mass in order to increase the acceleration??

8. Sep 16, 2013

### Staff: Mentor

Is it easier to push a car, or to push a small stone?
Which one has a larger mass?

9. Sep 16, 2013

### CWatters

Hints:

* The maximum thrust (a.k.a. force) that the engine can produce is fixed.
* The mass of the plane includes the variable mass of the passengers & baggage and fuel.
* Newtons Second law (google it)

10. Sep 17, 2013

### Molly1235

Obviously a stone...so you'd decrease the mass? Acceleration = force/mass and force is fixed, so yeah! Smaller mass = larger acceleration! I think I understand now, thank you!!

11. Sep 17, 2013

### CWatters

At some airports in developing countries they can't take off at maximum weight (particularly when its hot and/or the runway is at high altitude). They either have to leave some passengers & baggage behind or take less fuel to reduce weight and plan a stop somewhere to refuel.